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Mail: bech32 error analysis
Introduction
------------
Bech32's checksum algorithm was designed to be strong against substitution
errors, but it also provides some protection against more general classes of
errors. The final constant M that is XOR'ed into the checksum influences that
protection. BIP173 today uses M=1, but it is now known that this has a
weakness: if the final character is a "p", any number of "q" characters can be
inserted or erased right before it, without invalidating the checksum.
As it was recognized that other constants do not have this issue, the obvious
question is whether this is the only possible type of weakness, and if not, if
there is an optimal constant to use that minimizes the largest number of
weaknesses.
Since my last mail I've realized that it is actually possible to analyse the
behavior of these final constants under a wide variety of error classes
(substitutions, deletions, insertions, swaps, duplications) programatically.
Greg Maxwell and I have used this to perform an exhaustive analysis of certain
error patterns for all 2^30 possible M values, selected a number of criteria
to optimize for, and conclude that we should use as constant:
M = 0x2bc830a3
The code used to do this analysis, as well as the code used to verify some
expected properties of the final result, and more, can be found on
https://gist.github.com/sipa/14c248c288c3880a3b191f978a34508e
See results_final.txt to see how this constant compares with the previously
suggested constants 1, 0x3fffffff, and 0x3fefffff.
Properties
----------
If we define an error as a deletion of one position, a swap of adjacent
positions, a substitution in a specific position with a random character, an
insertion of one random character in a specific position, or a duplication of
the character in a specific position, then this M constant above gives us the
following properties:
* For generic HRPs and errors that don't affect the first 6 data characters,
or alternatively averaged over all HRPs (see details futher):
* Always detected:
* (P) Up to 4 substitution errors (true for any constant).
* (Q) Any valid code with the new constant, fed without modification to
software that uses the old constant 1 (true for any constant).
* Any error pattern has failure to detect probability <= 2^-30:
* (L) Any number of errors restricted to a single window of up to 4
characters.
* (B) Up to two errors restricted to a window of up to 68 characters.
* (D) Any one error made to a valid code with the new constant, and fed to
software that uses the old constant 1
* Most error patterns have probability <= 2^-30:
* (C) Up to two errors in general: out of 23926796 such error patterns,
0.0040% have probability 2^-25.
* (N) Up to three errors restricted to a window of up to 69 characters:
out of 284708444 such patterns, 0.033% have probability 2^-25.
* (O) Up to three errors in general: out of 295744442 such error patterns,
0.034% have probability 2^-25; 0.000065% have probability 2^-20.
* (G) Up to two errors made to a valid code with the new constant, and fed
to software that uses the old constant 1: out of 2831622 such error
patterns, 0.048% have probability 2^-25.
* Specifically for the bc1 HRP, with the BIP173 length restrictions:
* Always detected:
* (R) Up to 4 substitution errors (true for any constant).
* (A) Up to 3 substitution errors made to a valid code with the new
constant, and fed to software that uses the old constant 1.
* Any error pattern has failure to detect probability <= 2^-30:
* (E) Any one error.
* (F) Any one error made to a valid code with the new constant, and fed to
software that uses the old constant 1.
* (H) Up to two errors restricted to a window of 28 characters.
* Most error patterns have probability <= 2^-30:
* (J) Up to two errors in general: out of 455916 such error patterns,
0.039% have probability 2^-25; 0.0053% have 2^-20.
* (K) Any number of errors restricted to a window of 4 characters: out of
5813139 such error patterns, 0.0016% have probability 2^-25.
* (M) Up to three errors: out of 50713466 such error patterns, 0.078% have
probability 2^-25; 0.00063% have 2^-20.
* (I) Up to two errors made to a valid code with the new constant, and fed
to software that uses the old constant 1: out of 610683 such error
patterns, 0.092% have probability 2^-25; 0.00049% have probability
2^-20.
To give an idea of what these probabilities mean, consider the known BIP173
insertion issue. It admits an error pattern of 1 error (insertion in
penultimate position) that has a failure to detect probability of 2^-10:
it requires the final character to be 'p', and the inserted character to be
'q'. Assuming those are both random, we have a chance of 1 in 32*32 to hit it.
Note that the choice of *what* the error pattern is (whether it's insertion,
and where) isn't part of our probabilities: we try to make sure that *every*
pattern behaves well, not just randomly chosen ones, because presumably humans
make some kinds of errors more than others, and we don't know which ones.
All the analyzed patterns above are guaranteed to be detected with probability
2^-20 or better (and most are 2^-30). Of course, if we'd search for even
larger classes of errors, say any 4 independent errors of any type, we would
probably discover patterns with worse probabilities, but at that point the
probability of the pattern itself being hit should be taken into account.
The selection was made based on these same properties:
* Start with the set of all 2^30 constants.
* The generic properties (L), (B), (D), (C), (N), (O), and (G) were selected
for by rejecting all constants that left any worse error patterns (e.g.
all codes for which patterns matching (N) existed with failure probability
above 2^-25 were removed). All these restrictions are as strong as they
can be: making them over longer strings, wider windows, or more errors with
the same restrictions removes all remaining constants. This leaves us with
just 12054 acceptable constants.
* The same was then done for the bc1/BIP173 specific properties (A), (E), (J),
(F), (H), (K), (M), and (I). This reduces the set further to 79 acceptable
constants. The full analysis output for all of these can be found in
output.txt.
* Finally, the constant with the minimal number of worst-probability patterns
was chosen for the generic property (N). The single constant 0x2bc830a3
remains.
* This solution and a few of its expected properties were then validated using
a simple program that makes random errors (see the monte_carlo.py file).
Technical details
-----------------
For the purpose of this analysis, define an "error pattern" as a starting
length (of a valid string consisting of otherwise randomly chosen characters)
combined with a sequence of the following (in this order):
* 0 or more deletions of characters at specific positions (without
constraining what those characters are)
* 0 or more swaps of characters at specific positions with the character
following it
* 0 or more substitutions of characters at specific positions with a uniformly
randomly selected character
* 0 or more insertions of uniformly randomly selected characters at specific
positions
* 0 or more duplications of characters at specific positions (including
duplications of characters inserted/substituted in the previous steps)
Examples:
* "Start with a random valid 58 character string, remove the 17th character,
swap the 11th character with the 12th character, and insert a random
character in the 24th position" is an error pattern.
* "Replace the 17th through 24th characters in a 78 character string with
'aardvark'" is not an error pattern, because substituted characters have to
be random, and can't be specific values.
Given such a pattern, assign variable names to every input character, and to
every inserted/substituted character. For example, the pattern "Start with
a 6 character string, delete the 1st character, swap the 2nd and 3rd
character, and insert a random character between those" would be represented
as [v0 v1 v2 v3 v4 v5] and [v1 v3 v6 v2 v4 v5]. Treat these variables as
elements of GF(32), and write out the equations that both the first and second
list have a valid checksum. Due to the fact that BCH codes are linear, this is
just a linear set of equations over GF(32), and we can use Gaussian
elimination to find the size of the solution space. If the input and output
are the same length, we need to subtract the number of solutions for which the
input and output are exactly the same, which is easy to find with another set
of equations. Now compute the ratio of this number divided by (32^numvars /
32^6), where the 32^6 is due to the precondition that the input string is
valid. This gives us the probability of failure, assuming input and output are
random, apart from the known relation between the two, and the fact that both
are valid.
This technique has an important limitation: it can only reason about randomly-
chosen input strings, and the presence of the HRP and version numbers at the
start violates that assumption. These are not random, and we're forced to
make one of these concessions:
1) Ignore the problem, and treat the HRP as random. This lets us derive
properties that hold over all potential HRPs on average, but will thus fail
to account for the possibility that for a small numbers of potential HRPs
some error patterns may exist that behave worse. For technical reasons,
this averaging makes all constants behave identically for error patterns
that don't change the length of the string. Given that substitution/swap
only errors are already dealt with well due to the BCH design this is
perhaps not too important. One exception is frame-shifting errors (a
deletion in one place compensated with an insertion in another place).
2) Restrict analysis to error patterns that don't affect the first 6 actual
characters. Doing so "masks" the effect of the HRP completely.
3) Do analysis for specific HRPs only, allowing much more accurate statements,
but HRP-specific ones that may not hold for every HRP.
Our final selection primarily optimizes for 1) and 2) as those benefit all
potential uses of the encoding, but do optimize for 3) the "bc1" prefix
specifically (and the BIP173 length restriction) as a tiebreaker.
The code for this can be found under the link above, in const_analysis.cpp.
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <stdint.h>
#include <algorithm>
#include <array>
#include <string>
#include <type_traits>
#include <assert.h>
#include <numeric>
#include <immintrin.h>
constexpr int MAX_LEN = 89 + 6;
constexpr int DEGREE = 6;
typedef signed __int128 int128_t;
typedef unsigned __int128 uint128_t;
namespace {
inline uint64_t rdrand()
{
uint8_t ok;
uint64_t r;
while (1) {
__asm__ volatile (".byte 0x48, 0x0f, 0xc7, 0xf0; setc %1" : "=a"(r), "=q"(ok) :: "cc"); // rdrand %rax
if (ok) break;
__asm__ volatile ("pause" :);
}
return r;
}
class RNG {
uint64_t rng_state[2];
uint64_t rng_cache = 0;
int rng_bits = 0;
public:
RNG() {
rng_state[0] = rdrand();
rng_state[1] = rdrand();
}
using result_type = uint64_t;
constexpr uint64_t min() const { return 0; }
constexpr uint64_t max() const { return 0xFFFFFFFFFFFFFFFF; }
uint64_t operator()() {
rng_state[0] += 0x60bee2bee120fc15;
rng_state[1] += 0xa88615625dc1ee97;
uint128_t tmp1 = (uint128_t)rng_state[0] * 0xa3b195354a39b70d;
uint128_t tmp2 = (uint128_t)rng_state[1] * 0xa3b195354a39b70d;
uint64_t m1 = (tmp1 >> 64) ^ tmp1;
uint64_t m2 = (tmp2 >> 64) ^ tmp2;
tmp1 = (uint128_t)m1 * 0x1b03738712fad5c9;
tmp2 = (uint128_t)m2 * 0x1b03738712fad5c9;
return tmp1 ^ tmp2 ^ (tmp1 >> 64) ^ (tmp2 >> 64);
}
bool bit() {
if (rng_bits == 0) {
rng_cache = operator()();
rng_bits = 64;
}
bool ret = rng_cache & 1;
rng_cache >>= 1;
rng_bits -= 1;
return ret;
}
};
namespace GF {
namespace detail {
constexpr uint8_t MOD = 9;
constexpr int SIZE = 5;
constexpr uint8_t MASK = (1 << SIZE) - 1;
constexpr uint8_t mul2(uint8_t x) {
return ((x << 1) ^ ((MASK + 1 - (x >> (SIZE - 1))) & MOD)) & MASK;
}
constexpr struct Table {
uint8_t muldata[1 << SIZE][1 << SIZE];
uint8_t invdata[1 << SIZE];
constexpr Table() : muldata(), invdata() {
for (int x = 0; !(x >> SIZE); ++x) {
for (int y = 0; !(y >> SIZE); ++y) {
uint8_t res = 0, xv = x, yv = y;
for (int i = 0; i < SIZE; ++i) {
res ^= (MASK + 1 - (yv & 1)) & xv;
xv = mul2(xv);
yv >>= 1;
}
muldata[x][y] = res;
if (res == 1) invdata[x] = y;
}
}
}
} TABLE;
}
class Elem {
uint8_t val;
public:
constexpr Elem() : val(0) {}
constexpr Elem(uint8_t v) : val(v & detail::MASK) {}
Elem(const Elem& elem) = default;
constexpr inline Elem& operator=(const Elem& other) = default;
constexpr inline Elem& operator=(uint8_t v) { val = v & detail::MASK; return *this; }
constexpr explicit operator bool() const { return val != 0; }
constexpr bool inline operator==(Elem other) const { return val == other.val; }
constexpr bool inline operator!=(Elem other) const { return val != other.val; }
constexpr bool inline operator<(Elem other) const { return val < other.val; }
constexpr bool inline operator<=(Elem other) const { return val <= other.val; }
constexpr bool inline operator>(Elem other) const { return val > other.val; }
constexpr bool inline operator>=(Elem other) const { return val >= other.val; }
constexpr inline Elem operator+(Elem other) const { return Elem(val ^ other.val); }
constexpr inline Elem operator-(Elem other) const { return Elem(val ^ other.val); }
constexpr inline Elem operator*(Elem other) const { return Elem(detail::TABLE.muldata[val][other.val]); }
constexpr inline Elem operator/(Elem other) const { return Elem(detail::TABLE.muldata[val][detail::TABLE.invdata[other.val]]); }
constexpr inline Elem& operator+=(Elem other) { val ^= other.val; return *this; }
constexpr inline Elem& operator-=(Elem other) { val ^= other.val; return *this; }
constexpr inline Elem& operator*=(Elem other) { val = detail::TABLE.muldata[val][other.val]; return *this; }
constexpr inline Elem& operator/=(Elem other) { val = detail::TABLE.muldata[val][detail::TABLE.invdata[other.val]]; return *this; }
constexpr inline Elem inv() const { return Elem(detail::TABLE.invdata[val]); }
constexpr inline uint8_t to_int() const { return val; }
};
static_assert(std::is_trivially_copyable_v<Elem>);
}
constexpr std::array<GF::Elem, DEGREE> GENERATOR{18, 29, 21, 20, 22, 29};
constexpr std::array<GF::Elem, DEGREE> PREFIX{3, 2, 0, 3, 3, 1};
constexpr std::array<GF::Elem, DEGREE> MulX(const std::array<GF::Elem, DEGREE>& in) {
std::array<GF::Elem, DEGREE> ret;
for (int j = 0; j < DEGREE - 1; ++j) ret[j + 1] = in[j];
for (int j = 0; j < DEGREE; ++j) ret[j] -= in[DEGREE - 1] * GENERATOR[j];
return ret;
}
constexpr struct GeneratorShifts {
std::array<GF::Elem, DEGREE> data[MAX_LEN + 1];
std::array<GF::Elem, DEGREE> prefix_data[MAX_LEN + 1];
constexpr GeneratorShifts() : data() {
std::array<GF::Elem, DEGREE> entry{1, 0, 0, 0, 0, 0};
std::array<GF::Elem, DEGREE> prefix = PREFIX;
for (int i = 0; i <= MAX_LEN; ++i) {
data[i] = entry;
prefix_data[i] = prefix;
entry = MulX(entry);
prefix = MulX(prefix);
}
}
} GENERATOR_SHIFTS;
template<int ROWS, int COLS>
struct Mat {
GF::Elem cells[ROWS][COLS];
int rows;
int cols;
};
template<int ROWS, int COLS>
void PrintSol(Mat<ROWS, COLS>& mat, GF::Elem* vec) {
assert(mat.rows <= ROWS);
assert(mat.cols <= COLS);
for (int row = 0; row < mat.rows; ++row) {
printf("[");
for (int col = 0; col < mat.cols; ++col) {
printf("% 3i", (int)mat.cells[row][col].to_int());
}
printf("] x = [% 3i]\n", (int)vec[row].to_int());
}
printf("\n");
}
template<int ROWS, int COLS>
int SolutionRank(Mat<ROWS, COLS>& mat, GF::Elem* vec) {
assert(mat.rows <= ROWS);
assert(mat.cols <= COLS);
int pivot_r = 0, pivot_c = 0;
unsigned char swapspace[COLS];
while (pivot_r < mat.rows && pivot_c < mat.cols) {
// printf("pivot_r=%i pivot_c=%i\n", pivot_r, pivot_c);
// PrintSol(mat, vec);
int first_nonzero_r = pivot_r;
while (!mat.cells[first_nonzero_r][pivot_c] && first_nonzero_r < mat.rows) ++first_nonzero_r;
if (first_nonzero_r != mat.rows) {
if (first_nonzero_r != pivot_r) {
memcpy(swapspace, &mat.cells[pivot_r][pivot_c], mat.cols - pivot_c);
memcpy(&mat.cells[pivot_r][pivot_c], &mat.cells[first_nonzero_r][pivot_c], mat.cols - pivot_c);
memcpy(&mat.cells[first_nonzero_r][pivot_c], swapspace, mat.cols - pivot_c);
std::swap(vec[pivot_r], vec[first_nonzero_r]);
}
GF::Elem fact_pivot = mat.cells[pivot_r][pivot_c].inv();
for (int sweep_r = pivot_r + 1; sweep_r < mat.rows; ++sweep_r) {
if (mat.cells[sweep_r][pivot_c]) {
GF::Elem fact = fact_pivot * mat.cells[sweep_r][pivot_c];
mat.cells[sweep_r][pivot_c] = 0;
for (int sweep_c = pivot_c + 1; sweep_c < mat.cols; ++sweep_c) {
mat.cells[sweep_r][sweep_c] -= fact * mat.cells[pivot_r][sweep_c];
}
vec[sweep_r] -= fact * vec[pivot_r];
}
}
++pivot_r;
}
++pivot_c;
}
// printf("pivot_r=%i pivot_c=%i\n", pivot_r, pivot_c);
// PrintSol(mat, vec);
for (int vec_row = pivot_r; vec_row < mat.rows; ++vec_row) {
if (vec[vec_row]) return -1;
}
return pivot_r;
}
template<int VARS>
class UnionFind {
uint8_t parent[VARS];
int eq_rank;
public:
constexpr UnionFind(int v) : parent(), eq_rank(0) {
assert(v <= VARS);
for (int i = 0; i < v; ++i) {
parent[i] = i;
}
}
int Find(int x) {
while (parent[x] != x) {
int par = parent[x];
parent[x] = parent[par];
x = par;
}
return x;
}
void Union(int x, int y) {
int px = Find(x), py = Find(y);
if (px != py) {
parent[px] = py;
++eq_rank;
}
}
int GetRank() const {
return eq_rank;
}
};
int TransformWidth(int out_len, const uint8_t* out_vars, int in_len) {
int prefix_len = 0;
while (prefix_len < out_len && prefix_len < in_len && out_vars[prefix_len] == prefix_len) {
++prefix_len;
}
int suffix_len = 0;
while (suffix_len + prefix_len < out_len && suffix_len + prefix_len < in_len && out_vars[out_len - 1 - suffix_len] == in_len - 1 - suffix_len) {
++suffix_len;
}
return std::max(in_len, out_len) - prefix_len - suffix_len;
}
struct Analysis {
mutable std::array<GF::Elem, DEGREE> in_const;
mutable std::array<GF::Elem, DEGREE> out_const;
uint64_t in_const_val;
uint64_t out_const_val;
int max_deviation = 0;
int print_above_deviation = -2;
int max_width = -1;
int min_len = DEGREE + 2;
int max_len = MAX_LEN;
int fixed_suffix = 2;
int min_dels = 0;
int max_dels = DEGREE;
int min_swaps = 0;
int max_swaps = DEGREE;
int min_subs = 0;
int max_subs = DEGREE;
int min_ins = 0;
int max_ins = DEGREE;
int min_dups = 0;
int max_dups = DEGREE;
int min_len_change = -DEGREE;
int max_len_change = DEGREE;
int min_err = 1;
int max_err = 2;
bool bech32_len_restriction = false;
std::string report;
mutable std::array<uint64_t, 2 * DEGREE + 1> counts;
int Analyze(int out_len, const uint8_t* out_vars, int in_len, int num_vars) const {
Mat<2 * DEGREE, MAX_LEN + DEGREE> mat;
mat.rows = 2 * DEGREE;
mat.cols = num_vars;
for (int v = 0; v < in_len; ++v) {
for (int j = 0; j < DEGREE; ++j) {
mat.cells[j][v] = GENERATOR_SHIFTS.data[v][j];
}
}
for (int v = 0; v < out_len; ++v) {
for (int j = 0; j < DEGREE; ++j) {
mat.cells[j + DEGREE][out_vars[v]] += GENERATOR_SHIFTS.data[v][j];
}
}
std::array<GF::Elem, 2 * DEGREE> vec;
for (int j = 0; j < DEGREE; ++j) vec[j] = in_const[j] + GENERATOR_SHIFTS.prefix_data[in_len][j];
for (int j = 0; j < DEGREE; ++j) vec[j + DEGREE] = out_const[j] + GENERATOR_SHIFTS.prefix_data[out_len][j];
int sol_rank = SolutionRank(mat, vec.begin());
// printf(" * sol_rank=%i\n", sol_rank);
if (sol_rank < 0) return -1;
int limit = std::min(num_vars, 2 * DEGREE);
assert(sol_rank <= limit);
if (out_len == in_len && in_const_val == out_const_val) {
UnionFind<MAX_LEN + DEGREE> uf(num_vars);
for (int v = 0; v < in_len; ++v) {
if (out_vars[v] != v) uf.Union(v, out_vars[v]);
}
// printf(" * eq_rank=%i\n", uf.GetRank());
assert(sol_rank <= uf.GetRank() + DEGREE);
if (sol_rank == uf.GetRank() + DEGREE) return -1;
}
return limit - sol_rank;
}
int64_t Recurse(int dels, int swaps, int subs, int ins, int dups, int pos, int out_len, uint8_t* out_vars, int num_vars, int in_len, char* desc, int desc_len) const {
if (max_width >= 0) {
if (TransformWidth(out_len, out_vars, in_len) > max_width) return 0;
}
int64_t cnt = 0;
if (dels > 0) {
uint8_t new_out_vars[MAX_LEN + DEGREE];
desc[desc_len] = ',';
desc[desc_len + 1] = 'd';
desc[desc_len + 2] = 'e';
desc[desc_len + 3] = 'l';
while (pos + fixed_suffix < out_len) {
memcpy(new_out_vars, out_vars, pos);
memcpy(new_out_vars + pos, out_vars + pos + 1, out_len - 1 - pos);
desc[desc_len + 4] = '0' + (pos / 10);
desc[desc_len + 5] = '0' + (pos % 10);
int64_t ret = Recurse(dels - 1, swaps, subs, ins, dups, dels == 1 ? 0 : pos, out_len - 1, new_out_vars, num_vars, in_len, desc, desc_len + 6);
if (ret < 0) return -1;
cnt += ret;
++pos;
}
} else if (swaps > 0) {
uint8_t new_out_vars[MAX_LEN + DEGREE];
desc[desc_len] = ',';
desc[desc_len + 1] = 's';
desc[desc_len + 2] = 'w';
desc[desc_len + 3] = 'p';
while (pos + 1 + fixed_suffix < out_len) {
memcpy(new_out_vars, out_vars, pos);
new_out_vars[pos] = out_vars[pos + 1];
new_out_vars[pos + 1] = out_vars[pos];
memcpy(new_out_vars + pos + 2, out_vars + pos + 2, out_len - 2 - pos);
desc[desc_len + 4] = '0' + (pos / 10);
desc[desc_len + 5] = '0' + (pos % 10);
int64_t ret = Recurse(0, swaps - 1, subs, ins, dups, swaps == 1 ? 0 : pos + 1, out_len, new_out_vars, num_vars, in_len, desc, desc_len + 6);
if (ret < 0) return -1;
cnt += ret;
++pos;
}
} else if (subs > 0) {
desc[desc_len] = ',';
desc[desc_len + 1] = 's';
desc[desc_len + 2] = 'u';
desc[desc_len + 3] = 'b';
while (pos + fixed_suffix < out_len) {
uint8_t old = out_vars[pos];
out_vars[pos] = num_vars;
desc[desc_len + 4] = '0' + (pos / 10);
desc[desc_len + 5] = '0' + (pos % 10);
int64_t ret = Recurse(0, 0, subs - 1, ins, dups, subs == 1 ? 0 : pos + 1, out_len, out_vars, num_vars + 1, in_len, desc, desc_len + 6);
if (ret < 0) return -1;
cnt += ret;
out_vars[pos] = old;
++pos;
}
} else if (ins > 0) {
uint8_t new_out_vars[MAX_LEN + DEGREE];
desc[desc_len] = ',';
desc[desc_len + 1] = 'i';
desc[desc_len + 2] = 'n';
desc[desc_len + 3] = 's';
while (pos + fixed_suffix < out_len + 1) {
memcpy(new_out_vars, out_vars, pos);
new_out_vars[pos] = num_vars;
memcpy(new_out_vars + pos + 1, out_vars + pos, out_len - pos);
desc[desc_len + 4] = '0' + (pos / 10);
desc[desc_len + 5] = '0' + (pos % 10);
int64_t ret = Recurse(0, 0, 0, ins - 1, dups, ins == 1 ? 0 : pos + 1, out_len + 1, new_out_vars, num_vars + 1, in_len, desc, desc_len + 6);
if (ret < 0) return -1;
cnt += ret;
++pos;
}
} else if (dups > 0) {
uint8_t new_out_vars[MAX_LEN + DEGREE];
desc[desc_len] = ',';
desc[desc_len + 1] = 'd';
desc[desc_len + 2] = 'u';
desc[desc_len + 3] = 'p';
while (pos + fixed_suffix < out_len) {
memcpy(new_out_vars, out_vars, pos + 1);
new_out_vars[pos + 1] = out_vars[pos];
memcpy(new_out_vars + pos + 2, out_vars + pos + 1, out_len - pos - 1);
desc[desc_len + 4] = '0' + (pos / 10);
desc[desc_len + 5] = '0' + (pos % 10);
int64_t ret = Recurse(0, 0, 0, 0, dups - 1, dups == 1 ? 0 : pos + 1, out_len + 1, new_out_vars, num_vars, in_len, desc, desc_len + 6);
if (ret < 0) return -1;
cnt += ret;
++pos;
}
} else {
/* printf("* Running %.*s:", desc_len, desc);
for (int j = 0; j < out_len; ++j) {
printf(" %i", (int)out_vars[j]);
}
printf(" in_len=%i num_vars=%i\n", in_len, num_vars);*/
int deviation = Analyze(out_len, out_vars, in_len, num_vars);
++cnt;
#ifndef PRINT_ALL_FAILURES
if (print_above_deviation != -2 && deviation > print_above_deviation) {
printf("input_m=0x%llx output_m=0x%llx pat=%s desc=%.*s: deviation=%i\n", (unsigned long long)in_const_val, (unsigned long long)out_const_val, report.c_str(), desc_len, desc, deviation);
}
#endif
if (deviation > max_deviation) {
#ifdef PRINT_ALL_FAILURES
printf("input_m=0x%llx output_m=0x%llx par=%s desc=%.*s: deviation=%i\n", (unsigned long long)in_const_val, (unsigned long long)out_const_val, report.c_str(), desc_len, desc, deviation);
#endif
return -1;
}
++counts[deviation + 1];
}
return cnt;
}
bool Run() const {
for (int j = 0; j < DEGREE; ++j) in_const[j] = GF::Elem(in_const_val >> (5 * j));
for (int j = 0; j < DEGREE; ++j) out_const[j] = GF::Elem(out_const_val >> (5 * j));
for (auto& x : counts) x = 0;
for (int errors = min_err; errors <= max_err; ++errors) {
for (int in_len = min_len; in_len <= max_len; ++in_len) {
if (bech32_len_restriction && ((in_len % 8) == 0 || (in_len % 8) == 2 || (in_len % 8) == 5)) continue;
uint64_t cnt = 0;
char desc[5 + DEGREE * 6];
desc[0] = 'l';
desc[1] = 'e';
desc[2] = 'n';
desc[3] = '0' + (in_len / 10);
desc[4] = '0' + (in_len % 10);
for (int dels = min_dels; dels <= std::min(max_dels, errors); ++dels) {
if (dels >= DEGREE) continue;
for (int ins = min_ins; ins <= std::min(max_ins, errors - dels); ++ins) {
for (int dups = min_dups; dups <= std::min(max_dups, errors - dels - ins); ++dups) {
int out_len = in_len - dels + ins + dups;
if (bech32_len_restriction && ((out_len % 8) == 0 || (out_len % 8) == 2 || (out_len % 8) == 5)) continue;
if (out_len >= min_len && out_len <= max_len && out_len >= in_len + min_len_change && out_len <= in_len + max_len_change) {
for (int swaps = min_swaps; swaps <= std::min(max_swaps, errors - dels - ins - dups); ++swaps) {
int subs = errors - dels - ins - dups - swaps;
if (subs + ins >= DEGREE) continue;
if (in_const_val != out_const_val || swaps + subs != errors || (2 * swaps + subs) > 4) {
uint8_t out_vars[MAX_LEN + DEGREE];
for (int i = 0; i < in_len; ++i) out_vars[i] = i;
int64_t ret = Recurse(dels, swaps, subs, ins, dups, 0, in_len, out_vars, in_len, in_len, desc, 5);
if (ret < 0) return false;
cnt += ret;
}
}
}
}
}
}
// printf("# input_m=0x%llx output_m=0x%llx in_len=%i err=%i: tested %llu patterns\n", (unsigned long long)in_const_val, (unsigned long long)out_const_val, in_len, errors, (unsigned long long)cnt);
}
}
#ifdef REPORT
if (report.size()) {
std::string pr;
uint64_t total = std::accumulate(counts.begin(), counts.end(), (uint64_t)0);
for (size_t i = 0; i < std::size(counts); ++i) {
if (counts[i]) {
if (i == 0) {
pr += " pr(0)";
} else {
pr += " pr(2^-" + std::to_string(30 - 5 * (i - 1)) + ")";
}
pr += "=" + std::to_string(counts[i]) + "[" + std::to_string(100.0 * counts[i] / total) + "%]";
}
}
printf("const=0x%llx %s: total=%llu%s\n", (unsigned long long)in_const_val, report.c_str(), (unsigned long long)total, pr.c_str());
}
#endif
return true;
}
};
// Filter:
//
// - Averaged over all HRPs (or, restricted to errors that don't affect the first 6 data characters):
// - Within the new constant:
// - Up to 4 errors (only substitution): always detected (implied by generator choice)
// - Any errors, window <=4: <=2^-30 failure chance (test L)
// - Up to 2 errors:
// - Window <=68: <=2^-30 failure chance (test B)
// - Otherwise: <=2^-25 failure chance (test C)
// - Up to 3 errors:
// - Window <=69: <=2^-25 failure chance (test N)
// - Otherwise: <=2^-20 failure chance (test O)
// - From new constant to old constant(1)
// - Up to 1 error: <=2^-30 failure chance (test D)
// - Up to 2 errors: <=2^-25 failure chance (test G)
//
// - Specifically for the bc1 HRP, with bech32 length restrictions:
// - Within the new constant:
// - Up to 4 errors (only substitution): always detected (implied by generator choice)
// - Up to 1 error: <=2^-30 failure chance (test E)
// - Up to 2 errors, window <=28: <=2^-30 failure chance (test H)
// - Any errors within a window <=4: <=2^-25 failure chance (test K)
// - Up to 3 errors: <=2^-20 failure chance (test M; test J for up to 2 errors)
// - From new constant to old constant(1)
// - Up to 3 errors (only substitution): always detected (test A)
// - Up to 1 error: <=2^-30 failure chance (test F)
// - Up to 2 errors: <=2^-25 failure chance (test I)
void Analyse(uint64_t const_val) {
#ifndef SPECIFIC
// Test B: part 1 (start at len 78 for faster failure).
{
Analysis an;
an.min_len = 78;
an.max_len = 89;
an.min_err = 1;
an.max_err = 2;
an.max_width = 68;
an.max_deviation = 0;
an.fixed_suffix = 6;
an.in_const_val = const_val;
an.out_const_val = const_val;
if (!an.Run()) return;
}
// Test N1
{
Analysis an;
an.min_len = 78;
an.max_len = 89;
an.min_err = 3;
an.max_err = 3;
an.max_width = 69;
an.max_deviation = 1;
an.fixed_suffix = 6;
an.in_const_val = const_val;
an.out_const_val = const_val;
if (!an.Run()) return;
}
// Test D
{
Analysis an;
an.min_len = 6;
an.max_len = 94;
an.min_err = 1;
an.max_err = 1;
an.max_deviation = 0;
an.fixed_suffix = 6;
an.in_const_val = const_val;
an.out_const_val = 1;
an.report = "D";
if (!an.Run()) return;
}
// Test G
{
Analysis an;
an.min_len = 6;
an.max_len = 94;
an.min_err = 1;
an.max_err = 2;
an.max_deviation = 1;
an.fixed_suffix = 6;
an.in_const_val = const_val;
an.out_const_val = 1;
an.report = "G";
if (!an.Run()) return;
}
// Test L1
{
Analysis an;
an.min_len = 6;
an.max_len = 89;
an.min_err = 1;
an.max_err = 5;
an.max_width = 3;
an.max_deviation = 0;
an.fixed_suffix = 6;
an.in_const_val = const_val;
an.out_const_val = const_val;
if (!an.Run()) return;
}
// Test L2
{
Analysis an;
an.min_len = 6;
an.max_len = 94;
an.min_err = 1;
an.max_err = 7;
an.max_width = 4;
an.max_deviation = 0;
an.fixed_suffix = 6;
an.in_const_val = const_val;
an.out_const_val = const_val;
an.report = "L";
if (!an.Run()) return;
}
// Test C
{
Analysis an;
an.min_len = 6;
an.max_len = 94;
an.min_err = 1;
an.max_err = 2;
an.max_deviation = 1;
an.fixed_suffix = 6;
an.in_const_val = const_val;
an.out_const_val = const_val;
an.report = "C";
if (!an.Run()) return;
}
// Test O
{
Analysis an;
an.min_len = 6;
an.max_len = 94;
an.min_err = 1;
an.max_err = 3;
an.max_deviation = 2;
an.fixed_suffix = 6;
an.in_const_val = const_val;
an.out_const_val = const_val;
an.report = "O";
if (!an.Run()) return;
}
// Test B: part 2 (the whole range).
{
Analysis an;
an.min_len = 6;
an.max_len = 94;
an.min_err = 1;
an.max_err = 2;
an.max_width = 68;
an.max_deviation = 0;
an.fixed_suffix = 6;
an.in_const_val = const_val;
an.out_const_val = const_val;
an.report = "B";
if (!an.Run()) return;
}
// Test N2
{
Analysis an;
an.min_len = 6;
an.max_len = 94;
an.min_err = 1;
an.max_err = 3;
an.max_width = 69;
an.max_deviation = 1;
an.fixed_suffix = 6;
an.in_const_val = const_val;
an.out_const_val = const_val;
an.report = "N";
if (!an.Run()) return;
}
#endif
#ifndef GENERIC
// Test A (part 1/3)
{
Analysis an;
an.min_len = 11;
an.max_len = 71;
an.min_err = 1;
an.max_err = 1;
an.max_deviation = -1;
an.fixed_suffix = 0;
an.in_const_val = const_val;
an.out_const_val = 1;
an.max_dups = 0;
an.max_ins = 0;
an.max_swaps = 0;
an.max_dels = 0;
an.bech32_len_restriction = true;
if (!an.Run()) return;
}
// Test E
{
Analysis an;
an.min_len = 11;
an.max_len = 71;
an.min_err = 1;
an.max_err = 1;
an.max_deviation = 0;
an.fixed_suffix = 0;
an.in_const_val = const_val;
an.out_const_val = const_val;
an.bech32_len_restriction = true;
an.report = "E";
if (!an.Run()) return;
}
// Test F
{
Analysis an;
an.min_len = 11;
an.max_len = 71;
an.min_err = 1;
an.max_err = 1;
an.max_deviation = 0;
an.fixed_suffix = 0;
an.in_const_val = const_val;
an.out_const_val = 1;
an.bech32_len_restriction = true;
an.report = "F";
if (!an.Run()) return;
}
// Test A (part 2/3)
{
Analysis an;
an.min_len = 11;
an.max_len = 71;
an.min_err = 2;
an.max_err = 2;
an.max_deviation = -1;
an.fixed_suffix = 0;
an.in_const_val = const_val;
an.out_const_val = 1;
an.max_dups = 0;
an.max_ins = 0;
an.max_swaps = 0;
an.max_dels = 0;
an.bech32_len_restriction = true;
if (!an.Run()) return;
}
// Test H
{
Analysis an;
an.min_len = 11;
an.max_len = 71;
an.min_err = 1;
an.max_err = 2;
an.max_deviation = 0;
an.fixed_suffix = 0;
an.max_width = 28;
an.in_const_val = const_val;
an.out_const_val = const_val;
an.bech32_len_restriction = true;
an.report = "H";
if (!an.Run()) return;
}
// Test I
{
Analysis an;
an.min_len = 11;
an.max_len = 71;
an.min_err = 1;
an.max_err = 2;
an.max_deviation = 2;
an.fixed_suffix = 0;
an.in_const_val = const_val;
an.out_const_val = 1;
an.bech32_len_restriction = true;
an.report = "I";
if (!an.Run()) return;
}
// Test A (the whole range)
{
Analysis an;
an.min_len = 11;
an.max_len = 71;
an.min_err = 1;
an.max_err = 3;
an.max_deviation = -1;
an.fixed_suffix = 0;
an.in_const_val = const_val;
an.out_const_val = 1;
an.max_dups = 0;
an.max_ins = 0;
an.max_swaps = 0;
an.max_dels = 0;
an.bech32_len_restriction = true;
an.report = "A";
if (!an.Run()) return;
}
// Test J
{
Analysis an;
an.min_len = 11;
an.max_len = 71;
an.min_err = 1;
an.max_err = 2;
an.max_deviation = 2;
an.fixed_suffix = 0;
an.in_const_val = const_val;
an.out_const_val = const_val;
an.bech32_len_restriction = true;
an.report = "J";
if (!an.Run()) return;
}
// Test K
{
Analysis an;
an.min_len = 11;
an.max_len = 71;
an.min_err = 1;
an.max_err = 7;
an.max_width = 4;
an.max_deviation = 1;
an.fixed_suffix = 0;
an.in_const_val = const_val;
an.out_const_val = const_val;
an.bech32_len_restriction = true;
an.report = "K";
if (!an.Run()) return;
}
// Test M
{
Analysis an;
an.min_len = 11;
an.max_len = 71;
an.min_err = 1;
an.max_err = 3;
an.max_deviation = 2;
an.fixed_suffix = 0;
an.in_const_val = const_val;
an.out_const_val = const_val;
an.bech32_len_restriction = true;
an.report = "M";
if (!an.Run()) return;
}
#endif
printf("SOLUTION: 0x%llx\n", (unsigned long long)const_val);
}
}
int main(int argc, char** argv) {
setbuf(stdout, NULL);
if (argc > 1 && strcmp(argv[1], "-") == 0) {
char c[256];
while (fgets(c, 256, stdin)) {
uint64_t val = strtoull(c, nullptr, 0);
Analyse(val);
}
} else if (argc == 1) {
RNG rng;
while (true) {
Analyse(rng() & 0x3fffffff);
}
} else {
uint64_t low = strtoull(argv[1], nullptr, 0);
uint64_t high = low + 1;
if (argc > 2) high = strtoull(argv[2], nullptr, 0);
while (low != high) {
Analyse(low++);
}
}
return 0;
}
import random
CHARSET = "qpzry9x8gf2tvdw0s3jn54khce6mua7l"
HRP = "bc"
OLD_M = 1
NEW_M = 0x2bc830a3
def mulx(chk):
"""Multiply the polynomial represented by chk by x, mod g(x)."""
top = chk >> 25
chk = (chk & 0x1ffffff) << 5
chk ^= 0x3b6a57b2 if (top & 1) else 0
chk ^= 0x26508e6d if (top & 2) else 0
chk ^= 0x1ea119fa if (top & 4) else 0
chk ^= 0x3d4233dd if (top & 8) else 0
chk ^= 0x2a1462b3 if (top & 16) else 0
return chk
def bech32_verify_checksum(hrp, data, m):
"""Verify a checksum given HRP and converted data characters."""
chk = 1
for x in hrp:
chk = mulx(chk) ^ (ord(x) >> 5)
chk = mulx(chk)
for x in hrp:
chk = mulx(chk) ^ (ord(x) & 31)
for v in data:
chk = mulx(chk) ^ v
return chk == m
def bech32_compute_checksum(hrp, data, m):
"""Compute the checksum values given HRP and data."""
chk = 1
for x in hrp:
chk = mulx(chk) ^ (ord(x) >> 5)
chk = mulx(chk)
for x in hrp:
chk = mulx(chk) ^ (ord(x) & 31)
for p in range(len(data) - 6):
chk = mulx(chk) ^ data[p]
for _ in range(6):
chk = mulx(chk)
chk ^= m
return chk
def bech32_create_checksum(hrp, data, m):
"""Compute the checksum values given HRP and data."""
chk = bech32_compute_checksum(hrp, data, m)
return [(chk >> 5 * (5 - i)) & 31 for i in range(6)]
# Verify real BIP173
assert bech32_verify_checksum("bc", [CHARSET.find(d) for d in "qw508d6qejxtdg4y5r3zarvary0c5xw7kv8f3t4"], OLD_M)
assert bech32_create_checksum("bc", [CHARSET.find(d) for d in "qrp33g0q5c5txsp9arysrx4k6zdkfs4nce4xj0gdcccefvpysxf3q______"], OLD_M) == [CHARSET.find(d) for d in "ccfmv3"]
def subst(pos):
def tr(data, numvars):
return data[:pos] + [numvars] + data[pos+1:], numvars + 1
return tr
def delet(pos):
def tr(data, numvars):
return data[:pos] + data[pos+1:], numvars
return tr
def inser(pos):
def tr(data, numvars):
return data[:pos] + [numvars] + data[pos:], numvars + 1
return tr
def dupli(pos):
def tr(data, numvars):
return data[:pos+1] + [data[pos]] + data[pos+1:], numvars
return tr
def swap(pos):
def tr(data, numvars):
return data[:pos] + [data[pos+1], data[pos]] + data[pos+2:], numvars
return tr
def compute_pattern(inlen, trs):
pat = list(range(inlen))
numvars = inlen
for tr in trs:
pat, numvars = tr(pat, numvars)
return (inlen, pat, numvars)
def run_pattern(inlen, trs, in_m, out_m, hrp, iters):
inlen, pat, numvars = compute_pattern(inlen, trs)
rdata = [0 for _ in range(numvars)]
indata = [0 for _ in range(inlen)]
outdata = [0 for _ in range(len(pat))]
cnt = 0
actual_hrp = hrp
for _ in range(iters):
# Generate a random alphabetical HRP for every test if none provided.
if hrp is None:
actual_hrp = "".join(chr(97 + random.randrange(26)) for _ in range(random.randrange(6, 13)))
# Generate a valid random input & non-identity mutation to it.
while True:
# Generate the data symbols (excluding checksum).
for i in range(inlen - 6):
indata[i] = random.getrandbits(5)
# Fill in its corresponding checksum.
chk = bech32_compute_checksum(actual_hrp, indata, in_m)
indata[-6] = chk >> 25
indata[-5] = (chk >> 20) & 31
indata[-4] = (chk >> 15) & 31
indata[-3] = (chk >> 10) & 31
indata[-2] = (chk >> 5) & 31
indata[-1] = chk & 31
# Assert that it passes.
assert bech32_verify_checksum(actual_hrp, indata, in_m)
# Build the rdata array with all input & mutation symbols.
for i in range(inlen):
rdata[i] = indata[-1-i]
for i in range(inlen, numvars):
rdata[i] = random.getrandbits(5)
# Extract the output symbols from that.
for i in range(len(pat)):
outdata[-1-i] = rdata[pat[i]]
# If the result is identical the input, start over.
if indata != outdata or in_m != out_m:
break
# Count whether it passes validation still.
cnt += bech32_verify_checksum(actual_hrp, outdata, out_m)
return cnt
while True:
# Known patterns with 2^-20 probability for the bc1 HRP.
# print(run_pattern(67, [subst(23), subst(26), dupli(65)], NEW_M, NEW_M, HRP, 2**20))
# print(run_pattern(60, [delet(1), swap(28), dupli(58)], NEW_M, NEW_M, HRP, 2**20))
# print(run_pattern(39, [swap(31), inser(39), dupli(1)], NEW_M, NEW_M, HRP, 2**20))
# Known patterns with 2^-20 probability for the bc1 HRP, from new to old constant.
# print(run_pattern(60, [delet(57), subst(37)], NEW_M, OLD_M, HRP, 2**20))
# Known patterns with 2^-20 probability for random HRPs.
# print(run_pattern(79, [swap(15), subst(71), inser(1)], NEW_M, NEW_M, None, 2**20))
Chosen constant:
const=0x2bc830a3 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x2bc830a3 G: total=2831622 pr(0)=628056[22.180079%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1368[0.048312%]
const=0x2bc830a3 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x2bc830a3 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x2bc830a3 O: total=295744442 pr(0)=22987692[7.772823%] pr(2^-30)=272655828[92.193052%] pr(2^-25)=100730[0.034060%] pr(2^-20)=192[0.000065%]
const=0x2bc830a3 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x2bc830a3 N: total=284708444 pr(0)=22019858[7.734178%] pr(2^-30)=262593308[92.232357%] pr(2^-25)=95278[0.033465%]
const=0x2bc830a3 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x2bc830a3 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x2bc830a3 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x2bc830a3 I: total=610683 pr(0)=220552[36.115628%] pr(2^-30)=389564[63.791525%] pr(2^-25)=564[0.092356%] pr(2^-20)=3[0.000491%]
const=0x2bc830a3 A: total=708111 pr(0)=708111[100.000000%]
const=0x2bc830a3 J: total=455916 pr(0)=71679[15.721975%] pr(2^-30)=384037[84.234157%] pr(2^-25)=176[0.038604%] pr(2^-20)=24[0.005264%]
const=0x2bc830a3 K: total=5813139 pr(0)=4345033[74.745039%] pr(2^-30)=1468014[25.253379%] pr(2^-25)=92[0.001583%]
const=0x2bc830a3 M: total=50713466 pr(0)=7092439[13.985317%] pr(2^-30)=43581035[85.935824%] pr(2^-25)=39675[0.078234%] pr(2^-20)=317[0.000625%]
Previous proposals for modified constants:
const=0x3fefffff D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3fefffff G: total=2831622 pr(0)=628183[22.184564%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1241[0.043826%]
const=0x3fefffff L: total=19040076 pr(0)=10692488[56.157801%] pr(2^-30)=8347261[43.840482%] pr(2^-25)=327[0.001717%]
const=0x3fefffff C: total=2373450 pr(0)=184508[7.773831%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=522[0.021993%]
const=0x3fefffff O: total=295744442 pr(0)=22976379[7.768998%] pr(2^-30)=272655824[92.193051%] pr(2^-25)=109662[0.037080%] pr(2^-20)=2331[0.000788%] pr(2^-15)=246[0.000083%]
const=0x3fefffff B: total=2343190 pr(0)=180315[7.695279%] pr(2^-30)=2162392[92.284108%] pr(2^-25)=483[0.020613%]
const=0x3fefffff N: total=284708444 pr(0)=22007960[7.729999%] pr(2^-30)=262593304[92.232355%] pr(2^-25)=104876[0.036836%] pr(2^-20)=2058[0.000723%] pr(2^-15)=246[0.000086%]
const=0x3fefffff E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3fefffff F: total=5135 pr(0)=3637[70.827653%] pr(2^-30)=1495[29.113924%] pr(2^-25)=3[0.058423%]
const=0x3fefffff H: total=347707 pr(0)=58548[16.838315%] pr(2^-30)=289114[83.148743%] pr(2^-25)=45[0.012942%]
const=0x3fefffff I: total=610683 pr(0)=220640[36.130038%] pr(2^-30)=389564[63.791525%] pr(2^-25)=473[0.077454%] pr(2^-20)=6[0.000983%]
const=0x3fefffff A: total=708111 pr(0)=708111[100.000000%]
const=0x3fefffff J: total=455916 pr(0)=71581[15.700480%] pr(2^-30)=384037[84.234157%] pr(2^-25)=270[0.059221%] pr(2^-20)=28[0.006141%]
const=0x3fefffff K: total=5813139 pr(0)=4344971[74.743972%] pr(2^-30)=1468017[25.253430%] pr(2^-25)=151[0.002598%]
const=0x3fefffff M: total=50713466 pr(0)=7089928[13.980366%] pr(2^-30)=43581036[85.935826%] pr(2^-25)=41773[0.082371%] pr(2^-20)=681[0.001343%] pr(2^-15)=48[0.000095%]
const=0x3fffffff D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3fffffff G: total=2831622 pr(0)=628198[22.185094%] pr(2^-30)=2202200[77.771680%] pr(2^-25)=1224[0.043226%]
const=0x3fffffff L: total=19040076 pr(0)=10686436[56.126015%] pr(2^-30)=8347263[43.840492%] pr(2^-25)=6050[0.031775%] pr(2^-20)=327[0.001717%]
const=0x3fffffff C: total=2373450 pr(0)=183581[7.734774%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=711[0.029956%] pr(2^-20)=246[0.010365%] pr(2^-15)=246[0.010365%] pr(2^-10)=246[0.010365%]
const=0x3fffffff O: total=295744442 pr(0)=22885623[7.738310%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=143483[0.048516%] pr(2^-20)=31420[0.010624%] pr(2^-15)=26947[0.009112%] pr(2^-10)=1143[0.000386%]
const=0x3fffffff B: total=2343190 pr(0)=179364[7.654693%] pr(2^-30)=2162392[92.284108%] pr(2^-25)=696[0.029703%] pr(2^-20)=246[0.010499%] pr(2^-15)=246[0.010499%] pr(2^-10)=246[0.010499%]
const=0x3fffffff N: total=284708444 pr(0)=21920665[7.699338%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=137292[0.048222%] pr(2^-20)=30193[0.010605%] pr(2^-15)=25845[0.009078%] pr(2^-10)=1143[0.000401%]
const=0x3fffffff E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3fffffff F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3fffffff H: total=347707 pr(0)=58296[16.765840%] pr(2^-30)=289115[83.149031%] pr(2^-25)=152[0.043715%] pr(2^-20)=48[0.013805%] pr(2^-15)=48[0.013805%] pr(2^-10)=48[0.013805%]
const=0x3fffffff I: total=610683 pr(0)=220707[36.141009%] pr(2^-30)=389565[63.791689%] pr(2^-25)=405[0.066319%] pr(2^-20)=6[0.000983%]
const=0x3fffffff A: total=708111 pr(0)=708063[99.993221%] pr(2^-15)=48[0.006779%]
const=0x3fffffff J: total=455916 pr(0)=71370[15.654199%] pr(2^-30)=384038[84.234377%] pr(2^-25)=340[0.074575%] pr(2^-20)=72[0.015792%] pr(2^-15)=48[0.010528%] pr(2^-10)=48[0.010528%]
const=0x3fffffff K: total=5813139 pr(0)=4343783[74.723536%] pr(2^-30)=1468032[25.253688%] pr(2^-25)=1262[0.021709%] pr(2^-20)=62[0.001067%]
const=0x3fffffff M: total=50713466 pr(0)=7073780[13.948524%] pr(2^-30)=43581064[85.935881%] pr(2^-25)=47840[0.094334%] pr(2^-20)=5822[0.011480%] pr(2^-15)=4726[0.009319%] pr(2^-10)=234[0.000461%]
Original constant:
const=0x1 D: total=11660 pr(0)=263[2.255575%] pr(2^-30)=10387[89.082333%] pr(2^-25)=257[2.204117%] pr(2^-20)=254[2.178388%] pr(2^-15)=251[2.152659%] pr(2^-10)=248[2.126930%]
const=0x1 G: total=2373450 pr(0)=108752[4.582022%] pr(2^-30)=2188495[92.207335%] pr(2^-25)=26354[1.110367%] pr(2^-20)=24693[1.040384%] pr(2^-15)=24243[1.021425%] pr(2^-10)=913[0.038467%]
const=0x1 L: total=19040076 pr(0)=10282183[54.002846%] pr(2^-30)=8348023[43.844484%] pr(2^-25)=204886[1.076078%] pr(2^-20)=171149[0.898888%] pr(2^-15)=32103[0.168608%] pr(2^-10)=1732[0.009097%]
const=0x1 C: total=2373450 pr(0)=108752[4.582022%] pr(2^-30)=2188495[92.207335%] pr(2^-25)=26354[1.110367%] pr(2^-20)=24693[1.040384%] pr(2^-15)=24243[1.021425%] pr(2^-10)=913[0.038467%]
const=0x1 O: total=295744442 pr(0)=19693423[6.658933%] pr(2^-30)=272656212[92.193182%] pr(2^-25)=1734808[0.586590%] pr(2^-20)=1536219[0.519441%] pr(2^-15)=122207[0.041322%] pr(2^-10)=1573[0.000532%]
const=0x1 B: total=2343190 pr(0)=107532[4.589128%] pr(2^-30)=2162467[92.287309%] pr(2^-25)=25434[1.085443%] pr(2^-20)=23703[1.011570%] pr(2^-15)=23141[0.987585%] pr(2^-10)=913[0.038964%]
const=0x1 N: total=284708444 pr(0)=19033405[6.685227%] pr(2^-30)=262593692[92.232492%] pr(2^-25)=1584418[0.556505%] pr(2^-20)=1378499[0.484179%] pr(2^-15)=116857[0.041044%] pr(2^-10)=1573[0.000552%]
const=0x1 E: total=1976 pr(0)=289[14.625506%] pr(2^-30)=1496[75.708502%] pr(2^-25)=48[2.429150%] pr(2^-20)=48[2.429150%] pr(2^-15)=48[2.429150%] pr(2^-10)=47[2.378543%]
const=0x1 F: total=1976 pr(0)=289[14.625506%] pr(2^-30)=1496[75.708502%] pr(2^-25)=48[2.429150%] pr(2^-20)=48[2.429150%] pr(2^-15)=48[2.429150%] pr(2^-10)=47[2.378543%]
const=0x1 H: total=347707 pr(0)=49457[14.223757%] pr(2^-30)=289126[83.152194%] pr(2^-25)=3284[0.944473%] pr(2^-20)=2920[0.839788%] pr(2^-15)=2733[0.786007%] pr(2^-10)=187[0.053781%]
const=0x1 I: total=455916 pr(0)=58311[12.789856%] pr(2^-30)=384049[84.236789%] pr(2^-25)=4838[1.061160%] pr(2^-20)=4338[0.951491%] pr(2^-15)=4193[0.919687%] pr(2^-10)=187[0.041016%]
const=0x1 A: total=0
const=0x1 J: total=455916 pr(0)=58311[12.789856%] pr(2^-30)=384049[84.236789%] pr(2^-25)=4838[1.061160%] pr(2^-20)=4338[0.951491%] pr(2^-15)=4193[0.919687%] pr(2^-10)=187[0.041016%]
const=0x1 K: total=5813139 pr(0)=4256810[73.227391%] pr(2^-30)=1468118[25.255168%] pr(2^-25)=44201[0.760364%] pr(2^-20)=36644[0.630365%] pr(2^-15)=6996[0.120348%] pr(2^-10)=370[0.006365%]
const=0x1 M: total=50713466 pr(0)=6591484[12.997502%] pr(2^-30)=43581150[85.936051%] pr(2^-25)=289129[0.570123%] pr(2^-20)=229266[0.452081%] pr(2^-15)=22096[0.043570%] pr(2^-10)=341[0.000672%]
const=0x4f4fd6c A: total=708111 pr(0)=708111[100.000000%]
const=0x4f4fd6c B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x4f4fd6c C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x4f4fd6c D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x4f4fd6c E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x4f4fd6c F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x4f4fd6c G: total=2831622 pr(0)=628413[22.192687%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1011[0.035704%]
const=0x4f4fd6c H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x4f4fd6c I: total=610683 pr(0)=220645[36.130857%] pr(2^-30)=389564[63.791525%] pr(2^-25)=468[0.076636%] pr(2^-20)=6[0.000983%]
const=0x4f4fd6c J: total=455916 pr(0)=71687[15.723730%] pr(2^-30)=384037[84.234157%] pr(2^-25)=168[0.036849%] pr(2^-20)=24[0.005264%]
const=0x4f4fd6c K: total=5813139 pr(0)=4345039[74.745142%] pr(2^-30)=1468011[25.253327%] pr(2^-25)=89[0.001531%]
const=0x4f4fd6c L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x4f4fd6c M: total=50713466 pr(0)=7091876[13.984207%] pr(2^-30)=43581035[85.935824%] pr(2^-25)=40276[0.079419%] pr(2^-20)=279[0.000550%]
const=0x4f4fd6c N: total=284708444 pr(0)=22015347[7.732594%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99791[0.035050%]
const=0x4f4fd6c O: total=295744442 pr(0)=22983309[7.771341%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105115[0.035543%] pr(2^-20)=192[0.000065%]
const=0x4f4fd7e A: total=708111 pr(0)=708111[100.000000%]
const=0x4f4fd7e B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x4f4fd7e C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x4f4fd7e D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x4f4fd7e E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x4f4fd7e F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x4f4fd7e G: total=2831622 pr(0)=628516[22.196324%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=908[0.032066%]
const=0x4f4fd7e H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x4f4fd7e I: total=610683 pr(0)=220715[36.142319%] pr(2^-30)=389564[63.791525%] pr(2^-25)=397[0.065009%] pr(2^-20)=7[0.001146%]
const=0x4f4fd7e J: total=455916 pr(0)=71678[15.721756%] pr(2^-30)=384037[84.234157%] pr(2^-25)=177[0.038823%] pr(2^-20)=24[0.005264%]
const=0x4f4fd7e K: total=5813139 pr(0)=4345039[74.745142%] pr(2^-30)=1468011[25.253327%] pr(2^-25)=89[0.001531%]
const=0x4f4fd7e L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x4f4fd7e M: total=50713466 pr(0)=7092140[13.984727%] pr(2^-30)=43581044[85.935842%] pr(2^-25)=39986[0.078847%] pr(2^-20)=296[0.000584%]
const=0x4f4fd7e N: total=284708444 pr(0)=22018580[7.733729%] pr(2^-30)=262593308[92.232357%] pr(2^-25)=96556[0.033914%]
const=0x4f4fd7e O: total=295744442 pr(0)=22986278[7.772345%] pr(2^-30)=272655828[92.193052%] pr(2^-25)=102144[0.034538%] pr(2^-20)=192[0.000065%]
const=0x4f4fd7f A: total=708111 pr(0)=708111[100.000000%]
const=0x4f4fd7f B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x4f4fd7f C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x4f4fd7f D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x4f4fd7f E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x4f4fd7f F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x4f4fd7f G: total=2831622 pr(0)=628575[22.198408%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=849[0.029983%]
const=0x4f4fd7f H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x4f4fd7f I: total=610683 pr(0)=220674[36.135606%] pr(2^-30)=389565[63.791689%] pr(2^-25)=431[0.070577%] pr(2^-20)=13[0.002129%]
const=0x4f4fd7f J: total=455916 pr(0)=71687[15.723730%] pr(2^-30)=384037[84.234157%] pr(2^-25)=168[0.036849%] pr(2^-20)=24[0.005264%]
const=0x4f4fd7f K: total=5813139 pr(0)=4345039[74.745142%] pr(2^-30)=1468011[25.253327%] pr(2^-25)=89[0.001531%]
const=0x4f4fd7f L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x4f4fd7f M: total=50713466 pr(0)=7091670[13.983801%] pr(2^-30)=43581041[85.935836%] pr(2^-25)=40476[0.079813%] pr(2^-20)=279[0.000550%]
const=0x4f4fd7f N: total=284708444 pr(0)=22015360[7.732598%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99778[0.035046%]
const=0x4f4fd7f O: total=295744442 pr(0)=22983265[7.771326%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105159[0.035557%] pr(2^-20)=192[0.000065%]
const=0x508b662 A: total=708111 pr(0)=708111[100.000000%]
const=0x508b662 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x508b662 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x508b662 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x508b662 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x508b662 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x508b662 G: total=2831622 pr(0)=628389[22.191839%] pr(2^-30)=2202200[77.771680%] pr(2^-25)=1033[0.036481%]
const=0x508b662 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x508b662 I: total=610683 pr(0)=220661[36.133477%] pr(2^-30)=389563[63.791361%] pr(2^-25)=453[0.074179%] pr(2^-20)=6[0.000983%]
const=0x508b662 J: total=455916 pr(0)=71688[15.723949%] pr(2^-30)=384037[84.234157%] pr(2^-25)=163[0.035752%] pr(2^-20)=28[0.006141%]
const=0x508b662 K: total=5813139 pr(0)=4345039[74.745142%] pr(2^-30)=1468011[25.253327%] pr(2^-25)=89[0.001531%]
const=0x508b662 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x508b662 M: total=50713466 pr(0)=7091796[13.984049%] pr(2^-30)=43581042[85.935838%] pr(2^-25)=40320[0.079506%] pr(2^-20)=308[0.000607%]
const=0x508b662 N: total=284708444 pr(0)=22017770[7.733445%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=97368[0.034199%]
const=0x508b662 O: total=295744442 pr(0)=22985654[7.772134%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=102770[0.034750%] pr(2^-20)=192[0.000065%]
const=0x630d85b A: total=708111 pr(0)=708111[100.000000%]
const=0x630d85b B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x630d85b C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x630d85b D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x630d85b E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x630d85b F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x630d85b G: total=2831622 pr(0)=627446[22.158537%] pr(2^-30)=2202200[77.771680%] pr(2^-25)=1976[0.069783%]
const=0x630d85b H: total=347707 pr(0)=58591[16.850682%] pr(2^-30)=289116[83.149318%]
const=0x630d85b I: total=610683 pr(0)=220389[36.088936%] pr(2^-30)=389565[63.791689%] pr(2^-25)=724[0.118556%] pr(2^-20)=5[0.000819%]
const=0x630d85b J: total=455916 pr(0)=71681[15.722414%] pr(2^-30)=384039[84.234596%] pr(2^-25)=172[0.037726%] pr(2^-20)=24[0.005264%]
const=0x630d85b K: total=5813139 pr(0)=4345038[74.745125%] pr(2^-30)=1468011[25.253327%] pr(2^-25)=90[0.001548%]
const=0x630d85b L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x630d85b M: total=50713466 pr(0)=7092115[13.984678%] pr(2^-30)=43581035[85.935824%] pr(2^-25)=39990[0.078855%] pr(2^-20)=326[0.000643%]
const=0x630d85b N: total=284708444 pr(0)=22017906[7.733492%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=97232[0.034151%]
const=0x630d85b O: total=295744442 pr(0)=22985584[7.772110%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=102840[0.034773%] pr(2^-20)=192[0.000065%]
const=0x630d85c A: total=708111 pr(0)=708111[100.000000%]
const=0x630d85c B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x630d85c C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x630d85c D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x630d85c E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x630d85c F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x630d85c G: total=2831622 pr(0)=628474[22.194841%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=950[0.033550%]
const=0x630d85c H: total=347707 pr(0)=58591[16.850682%] pr(2^-30)=289116[83.149318%]
const=0x630d85c I: total=610683 pr(0)=220735[36.145594%] pr(2^-30)=389563[63.791361%] pr(2^-25)=380[0.062225%] pr(2^-20)=5[0.000819%]
const=0x630d85c J: total=455916 pr(0)=71673[15.720659%] pr(2^-30)=384039[84.234596%] pr(2^-25)=180[0.039481%] pr(2^-20)=24[0.005264%]
const=0x630d85c K: total=5813139 pr(0)=4345038[74.745125%] pr(2^-30)=1468011[25.253327%] pr(2^-25)=90[0.001548%]
const=0x630d85c L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x630d85c M: total=50713466 pr(0)=7092120[13.984688%] pr(2^-30)=43581036[85.935826%] pr(2^-25)=40011[0.078896%] pr(2^-20)=299[0.000590%]
const=0x630d85c N: total=284708444 pr(0)=22018306[7.733633%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96832[0.034011%]
const=0x630d85c O: total=295744442 pr(0)=22986256[7.772337%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=102168[0.034546%] pr(2^-20)=192[0.000065%]
const=0x687a19b A: total=708111 pr(0)=708111[100.000000%]
const=0x687a19b B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x687a19b C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x687a19b D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x687a19b E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x687a19b F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x687a19b G: total=2831622 pr(0)=627444[22.158466%] pr(2^-30)=2202206[77.771892%] pr(2^-25)=1972[0.069642%]
const=0x687a19b H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x687a19b I: total=610683 pr(0)=220470[36.102200%] pr(2^-30)=389566[63.791853%] pr(2^-25)=644[0.105456%] pr(2^-20)=3[0.000491%]
const=0x687a19b J: total=455916 pr(0)=71671[15.720220%] pr(2^-30)=384037[84.234157%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0x687a19b K: total=5813139 pr(0)=4345040[74.745159%] pr(2^-30)=1468010[25.253310%] pr(2^-25)=89[0.001531%]
const=0x687a19b L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x687a19b M: total=50713466 pr(0)=7091927[13.984307%] pr(2^-30)=43581030[85.935814%] pr(2^-25)=40218[0.079304%] pr(2^-20)=291[0.000574%]
const=0x687a19b N: total=284708444 pr(0)=22018812[7.733811%] pr(2^-30)=262593314[92.232359%] pr(2^-25)=96318[0.033830%]
const=0x687a19b O: total=295744442 pr(0)=22986810[7.772525%] pr(2^-30)=272655834[92.193054%] pr(2^-25)=101606[0.034356%] pr(2^-20)=192[0.000065%]
const=0x687a19d A: total=708111 pr(0)=708111[100.000000%]
const=0x687a19d B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x687a19d C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x687a19d D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x687a19d E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x687a19d F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x687a19d G: total=2831622 pr(0)=627101[22.146353%] pr(2^-30)=2202206[77.771892%] pr(2^-25)=2315[0.081755%]
const=0x687a19d H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x687a19d I: total=610683 pr(0)=220281[36.071251%] pr(2^-30)=389566[63.791853%] pr(2^-25)=836[0.136896%]
const=0x687a19d J: total=455916 pr(0)=71654[15.716492%] pr(2^-30)=384037[84.234157%] pr(2^-25)=197[0.043210%] pr(2^-20)=28[0.006141%]
const=0x687a19d K: total=5813139 pr(0)=4345040[74.745159%] pr(2^-30)=1468010[25.253310%] pr(2^-25)=89[0.001531%]
const=0x687a19d L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x687a19d M: total=50713466 pr(0)=7091414[13.983296%] pr(2^-30)=43581029[85.935812%] pr(2^-25)=40731[0.080316%] pr(2^-20)=292[0.000576%]
const=0x687a19d N: total=284708444 pr(0)=22018510[7.733705%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96628[0.033939%]
const=0x687a19d O: total=295744442 pr(0)=22986508[7.772423%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101916[0.034461%] pr(2^-20)=192[0.000065%]
const=0x7318408 A: total=708111 pr(0)=708111[100.000000%]
const=0x7318408 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x7318408 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x7318408 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x7318408 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x7318408 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x7318408 G: total=2831622 pr(0)=628523[22.196571%] pr(2^-30)=2202200[77.771680%] pr(2^-25)=899[0.031749%]
const=0x7318408 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x7318408 I: total=610683 pr(0)=220718[36.142811%] pr(2^-30)=389563[63.791361%] pr(2^-25)=385[0.063044%] pr(2^-20)=17[0.002784%]
const=0x7318408 J: total=455916 pr(0)=71678[15.721756%] pr(2^-30)=384037[84.234157%] pr(2^-25)=177[0.038823%] pr(2^-20)=24[0.005264%]
const=0x7318408 K: total=5813139 pr(0)=4345039[74.745142%] pr(2^-30)=1468011[25.253327%] pr(2^-25)=89[0.001531%]
const=0x7318408 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x7318408 M: total=50713466 pr(0)=7092139[13.984725%] pr(2^-30)=43581044[85.935842%] pr(2^-25)=39987[0.078849%] pr(2^-20)=296[0.000584%]
const=0x7318408 N: total=284708444 pr(0)=22018580[7.733729%] pr(2^-30)=262593308[92.232357%] pr(2^-25)=96556[0.033914%]
const=0x7318408 O: total=295744442 pr(0)=22986278[7.772345%] pr(2^-30)=272655828[92.193052%] pr(2^-25)=102144[0.034538%] pr(2^-20)=192[0.000065%]
const=0x731841a A: total=708111 pr(0)=708111[100.000000%]
const=0x731841a B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x731841a C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x731841a D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x731841a E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x731841a F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x731841a G: total=2831622 pr(0)=628540[22.197172%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=884[0.031219%]
const=0x731841a H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x731841a I: total=610683 pr(0)=220725[36.143957%] pr(2^-30)=389565[63.791689%] pr(2^-25)=387[0.063372%] pr(2^-20)=6[0.000983%]
const=0x731841a J: total=455916 pr(0)=71687[15.723730%] pr(2^-30)=384037[84.234157%] pr(2^-25)=168[0.036849%] pr(2^-20)=24[0.005264%]
const=0x731841a K: total=5813139 pr(0)=4345039[74.745142%] pr(2^-30)=1468011[25.253327%] pr(2^-25)=89[0.001531%]
const=0x731841a L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x731841a M: total=50713466 pr(0)=7091870[13.984195%] pr(2^-30)=43581039[85.935832%] pr(2^-25)=40278[0.079423%] pr(2^-20)=279[0.000550%]
const=0x731841a N: total=284708444 pr(0)=22015347[7.732594%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99791[0.035050%]
const=0x731841a O: total=295744442 pr(0)=22983309[7.771341%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105115[0.035543%] pr(2^-20)=192[0.000065%]
const=0x8a26c1f A: total=708111 pr(0)=708111[100.000000%]
const=0x8a26c1f B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x8a26c1f C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x8a26c1f D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x8a26c1f E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x8a26c1f F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x8a26c1f G: total=2831622 pr(0)=627928[22.175559%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1496[0.052832%]
const=0x8a26c1f H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x8a26c1f I: total=610683 pr(0)=220473[36.102692%] pr(2^-30)=389563[63.791361%] pr(2^-25)=637[0.104309%] pr(2^-20)=10[0.001638%]
const=0x8a26c1f J: total=455916 pr(0)=71692[15.724827%] pr(2^-30)=384037[84.234157%] pr(2^-25)=163[0.035752%] pr(2^-20)=24[0.005264%]
const=0x8a26c1f K: total=5813139 pr(0)=4345040[74.745159%] pr(2^-30)=1468010[25.253310%] pr(2^-25)=89[0.001531%]
const=0x8a26c1f L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x8a26c1f M: total=50713466 pr(0)=7092381[13.985203%] pr(2^-30)=43581038[85.935830%] pr(2^-25)=39744[0.078370%] pr(2^-20)=303[0.000597%]
const=0x8a26c1f N: total=284708444 pr(0)=22019484[7.734047%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=95654[0.033597%]
const=0x8a26c1f O: total=295744442 pr(0)=22987371[7.772714%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101005[0.034153%] pr(2^-20)=240[0.000081%]
const=0xb671569 A: total=708111 pr(0)=708111[100.000000%]
const=0xb671569 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0xb671569 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0xb671569 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0xb671569 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0xb671569 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0xb671569 G: total=2831622 pr(0)=628153[22.183505%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1271[0.044886%]
const=0xb671569 H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0xb671569 I: total=610683 pr(0)=220466[36.101545%] pr(2^-30)=389566[63.791853%] pr(2^-25)=642[0.105128%] pr(2^-20)=9[0.001474%]
const=0xb671569 J: total=455916 pr(0)=71691[15.724607%] pr(2^-30)=384038[84.234377%] pr(2^-25)=163[0.035752%] pr(2^-20)=24[0.005264%]
const=0xb671569 K: total=5813139 pr(0)=4345038[74.745125%] pr(2^-30)=1468012[25.253344%] pr(2^-25)=89[0.001531%]
const=0xb671569 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0xb671569 M: total=50713466 pr(0)=7092372[13.985185%] pr(2^-30)=43581040[85.935834%] pr(2^-25)=39751[0.078384%] pr(2^-20)=303[0.000597%]
const=0xb671569 N: total=284708444 pr(0)=22019484[7.734047%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=95654[0.033597%]
const=0xb671569 O: total=295744442 pr(0)=22987371[7.772714%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101005[0.034153%] pr(2^-20)=240[0.000081%]
const=0xdf25447 A: total=708111 pr(0)=708111[100.000000%]
const=0xdf25447 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0xdf25447 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0xdf25447 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0xdf25447 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0xdf25447 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0xdf25447 G: total=2831622 pr(0)=628027[22.179055%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1397[0.049336%]
const=0xdf25447 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0xdf25447 I: total=610683 pr(0)=220485[36.104657%] pr(2^-30)=389565[63.791689%] pr(2^-25)=633[0.103654%]
const=0xdf25447 J: total=455916 pr(0)=71671[15.720220%] pr(2^-30)=384037[84.234157%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0xdf25447 K: total=5813139 pr(0)=4345031[74.745004%] pr(2^-30)=1468018[25.253447%] pr(2^-25)=90[0.001548%]
const=0xdf25447 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0xdf25447 M: total=50713466 pr(0)=7091929[13.984311%] pr(2^-30)=43581032[85.935818%] pr(2^-25)=40214[0.079296%] pr(2^-20)=291[0.000574%]
const=0xdf25447 N: total=284708444 pr(0)=22018812[7.733811%] pr(2^-30)=262593314[92.232359%] pr(2^-25)=96318[0.033830%]
const=0xdf25447 O: total=295744442 pr(0)=22986810[7.772525%] pr(2^-30)=272655834[92.193054%] pr(2^-25)=101606[0.034356%] pr(2^-20)=192[0.000065%]
const=0xe372d24 A: total=708111 pr(0)=708111[100.000000%]
const=0xe372d24 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0xe372d24 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0xe372d24 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0xe372d24 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0xe372d24 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0xe372d24 G: total=2831622 pr(0)=628252[22.187001%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1172[0.041390%]
const=0xe372d24 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0xe372d24 I: total=610683 pr(0)=220688[36.137898%] pr(2^-30)=389564[63.791525%] pr(2^-25)=423[0.069267%] pr(2^-20)=8[0.001310%]
const=0xe372d24 J: total=455916 pr(0)=71667[15.719343%] pr(2^-30)=384037[84.234157%] pr(2^-25)=188[0.041236%] pr(2^-20)=24[0.005264%]
const=0xe372d24 K: total=5813139 pr(0)=4345035[74.745073%] pr(2^-30)=1468015[25.253396%] pr(2^-25)=89[0.001531%]
const=0xe372d24 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0xe372d24 M: total=50713466 pr(0)=7092052[13.984554%] pr(2^-30)=43581036[85.935826%] pr(2^-25)=40109[0.079089%] pr(2^-20)=269[0.000530%]
const=0xe372d24 N: total=284708444 pr(0)=22018512[7.733705%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96626[0.033939%]
const=0xe372d24 O: total=295744442 pr(0)=22986465[7.772408%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101959[0.034475%] pr(2^-20)=192[0.000065%]
const=0xe7d43ad A: total=708111 pr(0)=708111[100.000000%]
const=0xe7d43ad B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0xe7d43ad C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0xe7d43ad D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0xe7d43ad E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0xe7d43ad F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0xe7d43ad G: total=2831622 pr(0)=627446[22.158537%] pr(2^-30)=2202200[77.771680%] pr(2^-25)=1976[0.069783%]
const=0xe7d43ad H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0xe7d43ad I: total=610683 pr(0)=220350[36.082550%] pr(2^-30)=389565[63.791689%] pr(2^-25)=761[0.124615%] pr(2^-20)=7[0.001146%]
const=0xe7d43ad J: total=455916 pr(0)=71690[15.724388%] pr(2^-30)=384038[84.234377%] pr(2^-25)=164[0.035972%] pr(2^-20)=24[0.005264%]
const=0xe7d43ad K: total=5813139 pr(0)=4345035[74.745073%] pr(2^-30)=1468015[25.253396%] pr(2^-25)=89[0.001531%]
const=0xe7d43ad L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0xe7d43ad M: total=50713466 pr(0)=7091916[13.984286%] pr(2^-30)=43581042[85.935838%] pr(2^-25)=40191[0.079251%] pr(2^-20)=317[0.000625%]
const=0xe7d43ad N: total=284708444 pr(0)=22016995[7.733172%] pr(2^-30)=262593312[92.232358%] pr(2^-25)=98137[0.034469%]
const=0xe7d43ad O: total=295744442 pr(0)=22984895[7.771877%] pr(2^-30)=272655832[92.193054%] pr(2^-25)=103478[0.034989%] pr(2^-20)=237[0.000080%]
const=0x12fcee0a A: total=708111 pr(0)=708111[100.000000%]
const=0x12fcee0a B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x12fcee0a C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x12fcee0a D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x12fcee0a E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x12fcee0a F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x12fcee0a G: total=2831622 pr(0)=627956[22.176548%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1468[0.051843%]
const=0x12fcee0a H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x12fcee0a I: total=610683 pr(0)=220510[36.108750%] pr(2^-30)=389568[63.792180%] pr(2^-25)=605[0.099069%]
const=0x12fcee0a J: total=455916 pr(0)=71671[15.720220%] pr(2^-30)=384037[84.234157%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0x12fcee0a K: total=5813139 pr(0)=4345034[74.745056%] pr(2^-30)=1468016[25.253413%] pr(2^-25)=89[0.001531%]
const=0x12fcee0a L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x12fcee0a M: total=50713466 pr(0)=7091928[13.984309%] pr(2^-30)=43581027[85.935808%] pr(2^-25)=40220[0.079308%] pr(2^-20)=291[0.000574%]
const=0x12fcee0a N: total=284708444 pr(0)=22018812[7.733811%] pr(2^-30)=262593314[92.232359%] pr(2^-25)=96318[0.033830%]
const=0x12fcee0a O: total=295744442 pr(0)=22986810[7.772525%] pr(2^-30)=272655834[92.193054%] pr(2^-25)=101606[0.034356%] pr(2^-20)=192[0.000065%]
const=0x12fcee1c A: total=708111 pr(0)=708111[100.000000%]
const=0x12fcee1c B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x12fcee1c C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x12fcee1c D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x12fcee1c E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x12fcee1c F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x12fcee1c G: total=2831622 pr(0)=628516[22.196324%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=908[0.032066%]
const=0x12fcee1c H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x12fcee1c I: total=610683 pr(0)=220681[36.136752%] pr(2^-30)=389566[63.791853%] pr(2^-25)=430[0.070413%] pr(2^-20)=6[0.000983%]
const=0x12fcee1c J: total=455916 pr(0)=71667[15.719343%] pr(2^-30)=384037[84.234157%] pr(2^-25)=188[0.041236%] pr(2^-20)=24[0.005264%]
const=0x12fcee1c K: total=5813139 pr(0)=4345034[74.745056%] pr(2^-30)=1468016[25.253413%] pr(2^-25)=89[0.001531%]
const=0x12fcee1c L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x12fcee1c M: total=50713466 pr(0)=7091959[13.984371%] pr(2^-30)=43581033[85.935820%] pr(2^-25)=40190[0.079249%] pr(2^-20)=284[0.000560%]
const=0x12fcee1c N: total=284708444 pr(0)=22018920[7.733849%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96218[0.033795%]
const=0x12fcee1c O: total=295744442 pr(0)=22986909[7.772558%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101515[0.034325%] pr(2^-20)=192[0.000065%]
const=0x1423c1a7 A: total=708111 pr(0)=708111[100.000000%]
const=0x1423c1a7 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x1423c1a7 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x1423c1a7 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x1423c1a7 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x1423c1a7 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x1423c1a7 G: total=2831622 pr(0)=628063[22.180326%] pr(2^-30)=2202202[77.771751%] pr(2^-25)=1357[0.047923%]
const=0x1423c1a7 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x1423c1a7 I: total=610683 pr(0)=220499[36.106949%] pr(2^-30)=389565[63.791689%] pr(2^-25)=610[0.099888%] pr(2^-20)=9[0.001474%]
const=0x1423c1a7 J: total=455916 pr(0)=71671[15.720220%] pr(2^-30)=384037[84.234157%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0x1423c1a7 K: total=5813139 pr(0)=4345035[74.745073%] pr(2^-30)=1468015[25.253396%] pr(2^-25)=89[0.001531%]
const=0x1423c1a7 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x1423c1a7 M: total=50713466 pr(0)=7091625[13.983712%] pr(2^-30)=43581033[85.935820%] pr(2^-25)=40531[0.079922%] pr(2^-20)=277[0.000546%]
const=0x1423c1a7 N: total=284708444 pr(0)=22016995[7.733172%] pr(2^-30)=262593312[92.232358%] pr(2^-25)=98137[0.034469%]
const=0x1423c1a7 O: total=295744442 pr(0)=22984895[7.771877%] pr(2^-30)=272655832[92.193054%] pr(2^-25)=103478[0.034989%] pr(2^-20)=237[0.000080%]
const=0x17acd653 A: total=708111 pr(0)=708111[100.000000%]
const=0x17acd653 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x17acd653 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x17acd653 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x17acd653 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x17acd653 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x17acd653 G: total=2831622 pr(0)=628459[22.194311%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=965[0.034079%]
const=0x17acd653 H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x17acd653 I: total=610683 pr(0)=220685[36.137407%] pr(2^-30)=389565[63.791689%] pr(2^-25)=427[0.069922%] pr(2^-20)=6[0.000983%]
const=0x17acd653 J: total=455916 pr(0)=71690[15.724388%] pr(2^-30)=384038[84.234377%] pr(2^-25)=164[0.035972%] pr(2^-20)=24[0.005264%]
const=0x17acd653 K: total=5813139 pr(0)=4345039[74.745142%] pr(2^-30)=1468010[25.253310%] pr(2^-25)=90[0.001548%]
const=0x17acd653 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x17acd653 M: total=50713466 pr(0)=7091917[13.984288%] pr(2^-30)=43581038[85.935830%] pr(2^-25)=40194[0.079257%] pr(2^-20)=317[0.000625%]
const=0x17acd653 N: total=284708444 pr(0)=22016995[7.733172%] pr(2^-30)=262593312[92.232358%] pr(2^-25)=98137[0.034469%]
const=0x17acd653 O: total=295744442 pr(0)=22984895[7.771877%] pr(2^-30)=272655832[92.193054%] pr(2^-25)=103478[0.034989%] pr(2^-20)=237[0.000080%]
const=0x17acd659 A: total=708111 pr(0)=708111[100.000000%]
const=0x17acd659 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x17acd659 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x17acd659 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x17acd659 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x17acd659 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x17acd659 G: total=2831622 pr(0)=628552[22.197596%] pr(2^-30)=2202200[77.771680%] pr(2^-25)=870[0.030724%]
const=0x17acd659 H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x17acd659 I: total=610683 pr(0)=220708[36.141173%] pr(2^-30)=389564[63.791525%] pr(2^-25)=397[0.065009%] pr(2^-20)=14[0.002293%]
const=0x17acd659 J: total=455916 pr(0)=71700[15.726581%] pr(2^-30)=384038[84.234377%] pr(2^-25)=154[0.033778%] pr(2^-20)=24[0.005264%]
const=0x17acd659 K: total=5813139 pr(0)=4345039[74.745142%] pr(2^-30)=1468010[25.253310%] pr(2^-25)=90[0.001548%]
const=0x17acd659 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x17acd659 M: total=50713466 pr(0)=7092408[13.985256%] pr(2^-30)=43581039[85.935832%] pr(2^-25)=39727[0.078336%] pr(2^-20)=292[0.000576%]
const=0x17acd659 N: total=284708444 pr(0)=22018512[7.733705%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96626[0.033939%]
const=0x17acd659 O: total=295744442 pr(0)=22986465[7.772408%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101959[0.034475%] pr(2^-20)=192[0.000065%]
const=0x17e6b8d9 A: total=708111 pr(0)=708111[100.000000%]
const=0x17e6b8d9 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x17e6b8d9 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x17e6b8d9 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x17e6b8d9 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x17e6b8d9 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x17e6b8d9 G: total=2831622 pr(0)=628478[22.194982%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=946[0.033408%]
const=0x17e6b8d9 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x17e6b8d9 I: total=610683 pr(0)=220687[36.137734%] pr(2^-30)=389565[63.791689%] pr(2^-25)=420[0.068775%] pr(2^-20)=11[0.001801%]
const=0x17e6b8d9 J: total=455916 pr(0)=71667[15.719343%] pr(2^-30)=384037[84.234157%] pr(2^-25)=188[0.041236%] pr(2^-20)=24[0.005264%]
const=0x17e6b8d9 K: total=5813139 pr(0)=4345038[74.745125%] pr(2^-30)=1468011[25.253327%] pr(2^-25)=90[0.001548%]
const=0x17e6b8d9 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x17e6b8d9 M: total=50713466 pr(0)=7091966[13.984384%] pr(2^-30)=43581030[85.935814%] pr(2^-25)=40186[0.079241%] pr(2^-20)=284[0.000560%]
const=0x17e6b8d9 N: total=284708444 pr(0)=22018920[7.733849%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96218[0.033795%]
const=0x17e6b8d9 O: total=295744442 pr(0)=22986909[7.772558%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101515[0.034325%] pr(2^-20)=192[0.000065%]
const=0x17e6b8dd A: total=708111 pr(0)=708111[100.000000%]
const=0x17e6b8dd B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x17e6b8dd C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x17e6b8dd D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x17e6b8dd E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x17e6b8dd F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x17e6b8dd G: total=2831622 pr(0)=628291[22.188378%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1133[0.040012%]
const=0x17e6b8dd H: total=347707 pr(0)=58591[16.850682%] pr(2^-30)=289116[83.149318%]
const=0x17e6b8dd I: total=610683 pr(0)=220603[36.123979%] pr(2^-30)=389566[63.791853%] pr(2^-25)=509[0.083349%] pr(2^-20)=5[0.000819%]
const=0x17e6b8dd J: total=455916 pr(0)=71664[15.718685%] pr(2^-30)=384039[84.234596%] pr(2^-25)=189[0.041455%] pr(2^-20)=24[0.005264%]
const=0x17e6b8dd K: total=5813139 pr(0)=4345038[74.745125%] pr(2^-30)=1468011[25.253327%] pr(2^-25)=90[0.001548%]
const=0x17e6b8dd L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x17e6b8dd M: total=50713466 pr(0)=7091951[13.984355%] pr(2^-30)=43581039[85.935832%] pr(2^-25)=40194[0.079257%] pr(2^-20)=282[0.000556%]
const=0x17e6b8dd N: total=284708444 pr(0)=22017906[7.733492%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=97232[0.034151%]
const=0x17e6b8dd O: total=295744442 pr(0)=22985584[7.772110%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=102840[0.034773%] pr(2^-20)=192[0.000065%]
const=0x1c934d05 A: total=708111 pr(0)=708111[100.000000%]
const=0x1c934d05 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x1c934d05 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x1c934d05 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x1c934d05 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x1c934d05 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x1c934d05 G: total=2831622 pr(0)=628606[22.199503%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=818[0.028888%]
const=0x1c934d05 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x1c934d05 I: total=610683 pr(0)=220775[36.152144%] pr(2^-30)=389564[63.791525%] pr(2^-25)=341[0.055839%] pr(2^-20)=3[0.000491%]
const=0x1c934d05 J: total=455916 pr(0)=71667[15.719343%] pr(2^-30)=384037[84.234157%] pr(2^-25)=188[0.041236%] pr(2^-20)=24[0.005264%]
const=0x1c934d05 K: total=5813139 pr(0)=4345036[74.745090%] pr(2^-30)=1468014[25.253379%] pr(2^-25)=89[0.001531%]
const=0x1c934d05 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x1c934d05 M: total=50713466 pr(0)=7091970[13.984392%] pr(2^-30)=43581027[85.935808%] pr(2^-25)=40185[0.079239%] pr(2^-20)=284[0.000560%]
const=0x1c934d05 N: total=284708444 pr(0)=22018920[7.733849%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96218[0.033795%]
const=0x1c934d05 O: total=295744442 pr(0)=22986909[7.772558%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101515[0.034325%] pr(2^-20)=192[0.000065%]
const=0x1d256892 A: total=708111 pr(0)=708111[100.000000%]
const=0x1d256892 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x1d256892 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x1d256892 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x1d256892 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x1d256892 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x1d256892 G: total=2831622 pr(0)=628031[22.179196%] pr(2^-30)=2202200[77.771680%] pr(2^-25)=1391[0.049124%]
const=0x1d256892 H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x1d256892 I: total=610683 pr(0)=220534[36.112680%] pr(2^-30)=389565[63.791689%] pr(2^-25)=580[0.094976%] pr(2^-20)=4[0.000655%]
const=0x1d256892 J: total=455916 pr(0)=71686[15.723510%] pr(2^-30)=384038[84.234377%] pr(2^-25)=168[0.036849%] pr(2^-20)=24[0.005264%]
const=0x1d256892 K: total=5813139 pr(0)=4345036[74.745090%] pr(2^-30)=1468014[25.253379%] pr(2^-25)=89[0.001531%]
const=0x1d256892 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x1d256892 M: total=50713466 pr(0)=7091881[13.984217%] pr(2^-30)=43581032[85.935818%] pr(2^-25)=40274[0.079415%] pr(2^-20)=279[0.000550%]
const=0x1d256892 N: total=284708444 pr(0)=22015347[7.732594%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99791[0.035050%]
const=0x1d256892 O: total=295744442 pr(0)=22983309[7.771341%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105115[0.035543%] pr(2^-20)=192[0.000065%]
const=0x1ee011e4 A: total=708111 pr(0)=708111[100.000000%]
const=0x1ee011e4 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x1ee011e4 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x1ee011e4 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x1ee011e4 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x1ee011e4 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x1ee011e4 G: total=2831622 pr(0)=628133[22.182798%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1291[0.045592%]
const=0x1ee011e4 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x1ee011e4 I: total=610683 pr(0)=220590[36.121850%] pr(2^-30)=389567[63.792016%] pr(2^-25)=517[0.084659%] pr(2^-20)=9[0.001474%]
const=0x1ee011e4 J: total=455916 pr(0)=71687[15.723730%] pr(2^-30)=384037[84.234157%] pr(2^-25)=168[0.036849%] pr(2^-20)=24[0.005264%]
const=0x1ee011e4 K: total=5813139 pr(0)=4345037[74.745108%] pr(2^-30)=1468013[25.253361%] pr(2^-25)=89[0.001531%]
const=0x1ee011e4 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x1ee011e4 M: total=50713466 pr(0)=7091886[13.984227%] pr(2^-30)=43581028[85.935810%] pr(2^-25)=40273[0.079413%] pr(2^-20)=279[0.000550%]
const=0x1ee011e4 N: total=284708444 pr(0)=22015347[7.732594%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99791[0.035050%]
const=0x1ee011e4 O: total=295744442 pr(0)=22983309[7.771341%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105115[0.035543%] pr(2^-20)=192[0.000065%]
const=0x1f1c5ae6 A: total=708111 pr(0)=708111[100.000000%]
const=0x1f1c5ae6 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x1f1c5ae6 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x1f1c5ae6 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x1f1c5ae6 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x1f1c5ae6 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x1f1c5ae6 G: total=2831622 pr(0)=628297[22.188590%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1127[0.039801%]
const=0x1f1c5ae6 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x1f1c5ae6 I: total=610683 pr(0)=220703[36.140354%] pr(2^-30)=389563[63.791361%] pr(2^-25)=410[0.067138%] pr(2^-20)=7[0.001146%]
const=0x1f1c5ae6 J: total=455916 pr(0)=71701[15.726801%] pr(2^-30)=384037[84.234157%] pr(2^-25)=154[0.033778%] pr(2^-20)=24[0.005264%]
const=0x1f1c5ae6 K: total=5813139 pr(0)=4345030[74.744987%] pr(2^-30)=1468016[25.253413%] pr(2^-25)=93[0.001600%]
const=0x1f1c5ae6 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x1f1c5ae6 M: total=50713466 pr(0)=7092420[13.985280%] pr(2^-30)=43581041[85.935836%] pr(2^-25)=39704[0.078291%] pr(2^-20)=301[0.000594%]
const=0x1f1c5ae6 N: total=284708444 pr(0)=22018510[7.733705%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96628[0.033939%]
const=0x1f1c5ae6 O: total=295744442 pr(0)=22986508[7.772423%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101916[0.034461%] pr(2^-20)=192[0.000065%]
const=0x1f1c5af3 A: total=708111 pr(0)=708111[100.000000%]
const=0x1f1c5af3 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x1f1c5af3 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x1f1c5af3 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x1f1c5af3 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x1f1c5af3 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x1f1c5af3 G: total=2831622 pr(0)=627966[22.176901%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1458[0.051490%]
const=0x1f1c5af3 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x1f1c5af3 I: total=610683 pr(0)=220578[36.119885%] pr(2^-30)=389563[63.791361%] pr(2^-25)=536[0.087771%] pr(2^-20)=6[0.000983%]
const=0x1f1c5af3 J: total=455916 pr(0)=71701[15.726801%] pr(2^-30)=384037[84.234157%] pr(2^-25)=154[0.033778%] pr(2^-20)=24[0.005264%]
const=0x1f1c5af3 K: total=5813139 pr(0)=4345030[74.744987%] pr(2^-30)=1468016[25.253413%] pr(2^-25)=93[0.001600%]
const=0x1f1c5af3 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x1f1c5af3 M: total=50713466 pr(0)=7092405[13.985250%] pr(2^-30)=43581042[85.935838%] pr(2^-25)=39727[0.078336%] pr(2^-20)=292[0.000576%]
const=0x1f1c5af3 N: total=284708444 pr(0)=22018512[7.733705%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96626[0.033939%]
const=0x1f1c5af3 O: total=295744442 pr(0)=22986465[7.772408%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101959[0.034475%] pr(2^-20)=192[0.000065%]
const=0x1f1c5af8 A: total=708111 pr(0)=708111[100.000000%]
const=0x1f1c5af8 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x1f1c5af8 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x1f1c5af8 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x1f1c5af8 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x1f1c5af8 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x1f1c5af8 G: total=2831622 pr(0)=628139[22.183010%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1285[0.045380%]
const=0x1f1c5af8 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x1f1c5af8 I: total=610683 pr(0)=220557[36.116447%] pr(2^-30)=389565[63.791689%] pr(2^-25)=558[0.091373%] pr(2^-20)=3[0.000491%]
const=0x1f1c5af8 J: total=455916 pr(0)=71692[15.724827%] pr(2^-30)=384037[84.234157%] pr(2^-25)=163[0.035752%] pr(2^-20)=24[0.005264%]
const=0x1f1c5af8 K: total=5813139 pr(0)=4345030[74.744987%] pr(2^-30)=1468016[25.253413%] pr(2^-25)=93[0.001600%]
const=0x1f1c5af8 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x1f1c5af8 M: total=50713466 pr(0)=7092384[13.985209%] pr(2^-30)=43581033[85.935820%] pr(2^-25)=39746[0.078374%] pr(2^-20)=303[0.000597%]
const=0x1f1c5af8 N: total=284708444 pr(0)=22019484[7.734047%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=95654[0.033597%]
const=0x1f1c5af8 O: total=295744442 pr(0)=22987371[7.772714%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101005[0.034153%] pr(2^-20)=240[0.000081%]
const=0x1f1c5af9 A: total=708111 pr(0)=708111[100.000000%]
const=0x1f1c5af9 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x1f1c5af9 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x1f1c5af9 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x1f1c5af9 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x1f1c5af9 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x1f1c5af9 G: total=2831622 pr(0)=628056[22.180079%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1368[0.048312%]
const=0x1f1c5af9 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x1f1c5af9 I: total=610683 pr(0)=220536[36.113008%] pr(2^-30)=389565[63.791689%] pr(2^-25)=576[0.094321%] pr(2^-20)=6[0.000983%]
const=0x1f1c5af9 J: total=455916 pr(0)=71691[15.724607%] pr(2^-30)=384037[84.234157%] pr(2^-25)=164[0.035972%] pr(2^-20)=24[0.005264%]
const=0x1f1c5af9 K: total=5813139 pr(0)=4345030[74.744987%] pr(2^-30)=1468016[25.253413%] pr(2^-25)=93[0.001600%]
const=0x1f1c5af9 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x1f1c5af9 M: total=50713466 pr(0)=7091918[13.984290%] pr(2^-30)=43581038[85.935830%] pr(2^-25)=40193[0.079255%] pr(2^-20)=317[0.000625%]
const=0x1f1c5af9 N: total=284708444 pr(0)=22016995[7.733172%] pr(2^-30)=262593312[92.232358%] pr(2^-25)=98137[0.034469%]
const=0x1f1c5af9 O: total=295744442 pr(0)=22984895[7.771877%] pr(2^-30)=272655832[92.193054%] pr(2^-25)=103478[0.034989%] pr(2^-20)=237[0.000080%]
const=0x23cfc5c0 A: total=708111 pr(0)=708111[100.000000%]
const=0x23cfc5c0 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x23cfc5c0 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x23cfc5c0 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x23cfc5c0 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x23cfc5c0 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x23cfc5c0 G: total=2831622 pr(0)=628153[22.183505%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1271[0.044886%]
const=0x23cfc5c0 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x23cfc5c0 I: total=610683 pr(0)=220495[36.106294%] pr(2^-30)=389566[63.791853%] pr(2^-25)=613[0.100379%] pr(2^-20)=9[0.001474%]
const=0x23cfc5c0 J: total=455916 pr(0)=71671[15.720220%] pr(2^-30)=384037[84.234157%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0x23cfc5c0 K: total=5813139 pr(0)=4345036[74.745090%] pr(2^-30)=1468014[25.253379%] pr(2^-25)=89[0.001531%]
const=0x23cfc5c0 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x23cfc5c0 M: total=50713466 pr(0)=7091448[13.983363%] pr(2^-30)=43581035[85.935824%] pr(2^-25)=40698[0.080251%] pr(2^-20)=285[0.000562%]
const=0x23cfc5c0 N: total=284708444 pr(0)=22015347[7.732594%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99791[0.035050%]
const=0x23cfc5c0 O: total=295744442 pr(0)=22983309[7.771341%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105115[0.035543%] pr(2^-20)=192[0.000065%]
const=0x23cfc5df A: total=708111 pr(0)=708111[100.000000%]
const=0x23cfc5df B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x23cfc5df C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x23cfc5df D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x23cfc5df E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x23cfc5df F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x23cfc5df G: total=2831622 pr(0)=628348[22.190391%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1076[0.037999%]
const=0x23cfc5df H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x23cfc5df I: total=610683 pr(0)=220595[36.122669%] pr(2^-30)=389564[63.791525%] pr(2^-25)=518[0.084823%] pr(2^-20)=6[0.000983%]
const=0x23cfc5df J: total=455916 pr(0)=71671[15.720220%] pr(2^-30)=384037[84.234157%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0x23cfc5df K: total=5813139 pr(0)=4345036[74.745090%] pr(2^-30)=1468014[25.253379%] pr(2^-25)=89[0.001531%]
const=0x23cfc5df L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x23cfc5df M: total=50713466 pr(0)=7091922[13.984298%] pr(2^-30)=43581037[85.935828%] pr(2^-25)=40216[0.079300%] pr(2^-20)=291[0.000574%]
const=0x23cfc5df N: total=284708444 pr(0)=22018812[7.733811%] pr(2^-30)=262593314[92.232359%] pr(2^-25)=96318[0.033830%]
const=0x23cfc5df O: total=295744442 pr(0)=22986810[7.772525%] pr(2^-30)=272655834[92.193054%] pr(2^-25)=101606[0.034356%] pr(2^-20)=192[0.000065%]
const=0x24a6cfff A: total=708111 pr(0)=708111[100.000000%]
const=0x24a6cfff B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x24a6cfff C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x24a6cfff D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x24a6cfff E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x24a6cfff F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x24a6cfff G: total=2831622 pr(0)=628252[22.187001%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1172[0.041390%]
const=0x24a6cfff H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x24a6cfff I: total=610683 pr(0)=220674[36.135606%] pr(2^-30)=389567[63.792016%] pr(2^-25)=442[0.072378%]
const=0x24a6cfff J: total=455916 pr(0)=71678[15.721756%] pr(2^-30)=384037[84.234157%] pr(2^-25)=177[0.038823%] pr(2^-20)=24[0.005264%]
const=0x24a6cfff K: total=5813139 pr(0)=4345036[74.745090%] pr(2^-30)=1468014[25.253379%] pr(2^-25)=89[0.001531%]
const=0x24a6cfff L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x24a6cfff M: total=50713466 pr(0)=7092151[13.984749%] pr(2^-30)=43581036[85.935826%] pr(2^-25)=39983[0.078841%] pr(2^-20)=296[0.000584%]
const=0x24a6cfff N: total=284708444 pr(0)=22018580[7.733729%] pr(2^-30)=262593308[92.232357%] pr(2^-25)=96556[0.033914%]
const=0x24a6cfff O: total=295744442 pr(0)=22986278[7.772345%] pr(2^-30)=272655828[92.193052%] pr(2^-25)=102144[0.034538%] pr(2^-20)=192[0.000065%]
const=0x255a84f0 A: total=708111 pr(0)=708111[100.000000%]
const=0x255a84f0 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x255a84f0 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x255a84f0 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x255a84f0 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x255a84f0 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x255a84f0 G: total=2831622 pr(0)=629088[22.216525%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=336[0.011866%]
const=0x255a84f0 H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x255a84f0 I: total=610683 pr(0)=220916[36.175233%] pr(2^-30)=389566[63.791853%] pr(2^-25)=201[0.032914%]
const=0x255a84f0 J: total=455916 pr(0)=71690[15.724388%] pr(2^-30)=384038[84.234377%] pr(2^-25)=164[0.035972%] pr(2^-20)=24[0.005264%]
const=0x255a84f0 K: total=5813139 pr(0)=4345040[74.745159%] pr(2^-30)=1468010[25.253310%] pr(2^-25)=89[0.001531%]
const=0x255a84f0 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x255a84f0 M: total=50713466 pr(0)=7091916[13.984286%] pr(2^-30)=43581039[85.935832%] pr(2^-25)=40194[0.079257%] pr(2^-20)=317[0.000625%]
const=0x255a84f0 N: total=284708444 pr(0)=22016995[7.733172%] pr(2^-30)=262593312[92.232358%] pr(2^-25)=98137[0.034469%]
const=0x255a84f0 O: total=295744442 pr(0)=22984895[7.771877%] pr(2^-30)=272655832[92.193054%] pr(2^-25)=103478[0.034989%] pr(2^-20)=237[0.000080%]
const=0x2662ead4 A: total=708111 pr(0)=708111[100.000000%]
const=0x2662ead4 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x2662ead4 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x2662ead4 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x2662ead4 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x2662ead4 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x2662ead4 G: total=2831622 pr(0)=628730[22.203882%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=694[0.024509%]
const=0x2662ead4 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x2662ead4 I: total=610683 pr(0)=220849[36.164262%] pr(2^-30)=389565[63.791689%] pr(2^-25)=264[0.043230%] pr(2^-20)=5[0.000819%]
const=0x2662ead4 J: total=455916 pr(0)=71679[15.721975%] pr(2^-30)=384037[84.234157%] pr(2^-25)=176[0.038604%] pr(2^-20)=24[0.005264%]
const=0x2662ead4 K: total=5813139 pr(0)=4345038[74.745125%] pr(2^-30)=1468012[25.253344%] pr(2^-25)=89[0.001531%]
const=0x2662ead4 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x2662ead4 M: total=50713466 pr(0)=7092000[13.984451%] pr(2^-30)=43581036[85.935826%] pr(2^-25)=40105[0.079082%] pr(2^-20)=325[0.000641%]
const=0x2662ead4 N: total=284708444 pr(0)=22017255[7.733264%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=97883[0.034380%]
const=0x2662ead4 O: total=295744442 pr(0)=22985162[7.771968%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=103262[0.034916%] pr(2^-20)=192[0.000065%]
const=0x26d59308 A: total=708111 pr(0)=708111[100.000000%]
const=0x26d59308 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x26d59308 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x26d59308 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x26d59308 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x26d59308 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x26d59308 G: total=2831622 pr(0)=628072[22.180644%] pr(2^-30)=2202200[77.771680%] pr(2^-25)=1350[0.047676%]
const=0x26d59308 H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x26d59308 I: total=610683 pr(0)=220583[36.120704%] pr(2^-30)=389564[63.791525%] pr(2^-25)=536[0.087771%]
const=0x26d59308 J: total=455916 pr(0)=71665[15.718904%] pr(2^-30)=384038[84.234377%] pr(2^-25)=189[0.041455%] pr(2^-20)=24[0.005264%]
const=0x26d59308 K: total=5813139 pr(0)=4345040[74.745159%] pr(2^-30)=1468009[25.253293%] pr(2^-25)=90[0.001548%]
const=0x26d59308 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x26d59308 M: total=50713466 pr(0)=7091967[13.984386%] pr(2^-30)=43581027[85.935808%] pr(2^-25)=40190[0.079249%] pr(2^-20)=282[0.000556%]
const=0x26d59308 N: total=284708444 pr(0)=22017906[7.733492%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=97232[0.034151%]
const=0x26d59308 O: total=295744442 pr(0)=22985584[7.772110%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=102840[0.034773%] pr(2^-20)=192[0.000065%]
const=0x26d59318 A: total=708111 pr(0)=708111[100.000000%]
const=0x26d59318 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x26d59318 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x26d59318 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x26d59318 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x26d59318 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x26d59318 G: total=2831622 pr(0)=628387[22.191769%] pr(2^-30)=2202200[77.771680%] pr(2^-25)=1035[0.036551%]
const=0x26d59318 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x26d59318 I: total=610683 pr(0)=220760[36.149688%] pr(2^-30)=389563[63.791361%] pr(2^-25)=357[0.058459%] pr(2^-20)=3[0.000491%]
const=0x26d59318 J: total=455916 pr(0)=71671[15.720220%] pr(2^-30)=384037[84.234157%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0x26d59318 K: total=5813139 pr(0)=4345040[74.745159%] pr(2^-30)=1468009[25.253293%] pr(2^-25)=90[0.001548%]
const=0x26d59318 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x26d59318 M: total=50713466 pr(0)=7092172[13.984791%] pr(2^-30)=43581027[85.935808%] pr(2^-25)=39983[0.078841%] pr(2^-20)=284[0.000560%]
const=0x26d59318 N: total=284708444 pr(0)=22019123[7.733920%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96015[0.033724%]
const=0x26d59318 O: total=295744442 pr(0)=22986648[7.772470%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101776[0.034413%] pr(2^-20)=192[0.000065%]
const=0x2763b69b A: total=708111 pr(0)=708111[100.000000%]
const=0x2763b69b B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x2763b69b C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x2763b69b D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x2763b69b E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x2763b69b F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x2763b69b G: total=2831622 pr(0)=628126[22.182551%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1298[0.045839%]
const=0x2763b69b H: total=347707 pr(0)=58590[16.850394%] pr(2^-30)=289117[83.149606%]
const=0x2763b69b I: total=610683 pr(0)=220554[36.115955%] pr(2^-30)=389567[63.792016%] pr(2^-25)=556[0.091046%] pr(2^-20)=6[0.000983%]
const=0x2763b69b J: total=455916 pr(0)=71684[15.723072%] pr(2^-30)=384040[84.234815%] pr(2^-25)=168[0.036849%] pr(2^-20)=24[0.005264%]
const=0x2763b69b K: total=5813139 pr(0)=4345039[74.745142%] pr(2^-30)=1468011[25.253327%] pr(2^-25)=89[0.001531%]
const=0x2763b69b L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x2763b69b M: total=50713466 pr(0)=7091879[13.984213%] pr(2^-30)=43581036[85.935826%] pr(2^-25)=40272[0.079411%] pr(2^-20)=279[0.000550%]
const=0x2763b69b N: total=284708444 pr(0)=22015347[7.732594%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99791[0.035050%]
const=0x2763b69b O: total=295744442 pr(0)=22983309[7.771341%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105115[0.035543%] pr(2^-20)=192[0.000065%]
const=0x28ba3016 A: total=708111 pr(0)=708111[100.000000%]
const=0x28ba3016 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x28ba3016 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x28ba3016 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x28ba3016 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x28ba3016 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x28ba3016 G: total=2831622 pr(0)=628523[22.196571%] pr(2^-30)=2202200[77.771680%] pr(2^-25)=899[0.031749%]
const=0x28ba3016 H: total=347707 pr(0)=58589[16.850107%] pr(2^-30)=289118[83.149893%]
const=0x28ba3016 I: total=610683 pr(0)=220799[36.156074%] pr(2^-30)=389565[63.791689%] pr(2^-25)=319[0.052237%]
const=0x28ba3016 J: total=455916 pr(0)=71663[15.718466%] pr(2^-30)=384041[84.235035%] pr(2^-25)=188[0.041236%] pr(2^-20)=24[0.005264%]
const=0x28ba3016 K: total=5813139 pr(0)=4345028[74.744953%] pr(2^-30)=1468020[25.253482%] pr(2^-25)=91[0.001565%]
const=0x28ba3016 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x28ba3016 M: total=50713466 pr(0)=7092041[13.984532%] pr(2^-30)=43581037[85.935828%] pr(2^-25)=40119[0.079109%] pr(2^-20)=269[0.000530%]
const=0x28ba3016 N: total=284708444 pr(0)=22018512[7.733705%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96626[0.033939%]
const=0x28ba3016 O: total=295744442 pr(0)=22986465[7.772408%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101959[0.034475%] pr(2^-20)=192[0.000065%]
const=0x28ba301c A: total=708111 pr(0)=708111[100.000000%]
const=0x28ba301c B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x28ba301c C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x28ba301c D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x28ba301c E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x28ba301c F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x28ba301c G: total=2831622 pr(0)=627928[22.175559%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1496[0.052832%]
const=0x28ba301c H: total=347707 pr(0)=58589[16.850107%] pr(2^-30)=289118[83.149893%]
const=0x28ba301c I: total=610683 pr(0)=220483[36.104329%] pr(2^-30)=389565[63.791689%] pr(2^-25)=629[0.102999%] pr(2^-20)=6[0.000983%]
const=0x28ba301c J: total=455916 pr(0)=71667[15.719343%] pr(2^-30)=384041[84.235035%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0x28ba301c K: total=5813139 pr(0)=4345028[74.744953%] pr(2^-30)=1468020[25.253482%] pr(2^-25)=91[0.001565%]
const=0x28ba301c L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x28ba301c M: total=50713466 pr(0)=7091432[13.983331%] pr(2^-30)=43581041[85.935836%] pr(2^-25)=40708[0.080271%] pr(2^-20)=285[0.000562%]
const=0x28ba301c N: total=284708444 pr(0)=22015347[7.732594%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99791[0.035050%]
const=0x28ba301c O: total=295744442 pr(0)=22983309[7.771341%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105115[0.035543%] pr(2^-20)=192[0.000065%]
const=0x290c1591 A: total=708111 pr(0)=708111[100.000000%]
const=0x290c1591 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x290c1591 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x290c1591 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x290c1591 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x290c1591 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x290c1591 G: total=2831622 pr(0)=628296[22.188555%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1128[0.039836%]
const=0x290c1591 H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x290c1591 I: total=610683 pr(0)=220697[36.139372%] pr(2^-30)=389565[63.791689%] pr(2^-25)=419[0.068612%] pr(2^-20)=2[0.000328%]
const=0x290c1591 J: total=455916 pr(0)=71686[15.723510%] pr(2^-30)=384038[84.234377%] pr(2^-25)=168[0.036849%] pr(2^-20)=24[0.005264%]
const=0x290c1591 K: total=5813139 pr(0)=4345028[74.744953%] pr(2^-30)=1468020[25.253482%] pr(2^-25)=91[0.001565%]
const=0x290c1591 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x290c1591 M: total=50713466 pr(0)=7091665[13.983791%] pr(2^-30)=43581041[85.935836%] pr(2^-25)=40481[0.079823%] pr(2^-20)=279[0.000550%]
const=0x290c1591 N: total=284708444 pr(0)=22015360[7.732598%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99778[0.035046%]
const=0x290c1591 O: total=295744442 pr(0)=22983265[7.771326%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105159[0.035557%] pr(2^-20)=192[0.000065%]
const=0x2b3527f6 A: total=708111 pr(0)=708111[100.000000%]
const=0x2b3527f6 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x2b3527f6 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x2b3527f6 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x2b3527f6 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x2b3527f6 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x2b3527f6 G: total=2831622 pr(0)=628552[22.197596%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=872[0.030795%]
const=0x2b3527f6 H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x2b3527f6 I: total=610683 pr(0)=220749[36.147887%] pr(2^-30)=389565[63.791689%] pr(2^-25)=363[0.059442%] pr(2^-20)=6[0.000983%]
const=0x2b3527f6 J: total=455916 pr(0)=71700[15.726581%] pr(2^-30)=384038[84.234377%] pr(2^-25)=154[0.033778%] pr(2^-20)=24[0.005264%]
const=0x2b3527f6 K: total=5813139 pr(0)=4345040[74.745159%] pr(2^-30)=1468010[25.253310%] pr(2^-25)=89[0.001531%]
const=0x2b3527f6 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x2b3527f6 M: total=50713466 pr(0)=7092421[13.985282%] pr(2^-30)=43581041[85.935836%] pr(2^-25)=39703[0.078289%] pr(2^-20)=301[0.000594%]
const=0x2b3527f6 N: total=284708444 pr(0)=22018510[7.733705%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96628[0.033939%]
const=0x2b3527f6 O: total=295744442 pr(0)=22986508[7.772423%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101916[0.034461%] pr(2^-20)=192[0.000065%]
const=0x2bc830a3 A: total=708111 pr(0)=708111[100.000000%]
const=0x2bc830a3 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x2bc830a3 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x2bc830a3 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x2bc830a3 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x2bc830a3 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x2bc830a3 G: total=2831622 pr(0)=628056[22.180079%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1368[0.048312%]
const=0x2bc830a3 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x2bc830a3 I: total=610683 pr(0)=220552[36.115628%] pr(2^-30)=389564[63.791525%] pr(2^-25)=564[0.092356%] pr(2^-20)=3[0.000491%]
const=0x2bc830a3 J: total=455916 pr(0)=71679[15.721975%] pr(2^-30)=384037[84.234157%] pr(2^-25)=176[0.038604%] pr(2^-20)=24[0.005264%]
const=0x2bc830a3 K: total=5813139 pr(0)=4345033[74.745039%] pr(2^-30)=1468014[25.253379%] pr(2^-25)=92[0.001583%]
const=0x2bc830a3 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x2bc830a3 M: total=50713466 pr(0)=7092439[13.985317%] pr(2^-30)=43581035[85.935824%] pr(2^-25)=39675[0.078234%] pr(2^-20)=317[0.000625%]
const=0x2bc830a3 N: total=284708444 pr(0)=22019858[7.734178%] pr(2^-30)=262593308[92.232357%] pr(2^-25)=95278[0.033465%]
const=0x2bc830a3 O: total=295744442 pr(0)=22987692[7.772823%] pr(2^-30)=272655828[92.193052%] pr(2^-25)=100730[0.034060%] pr(2^-20)=192[0.000065%]
const=0x2bc830b2 A: total=708111 pr(0)=708111[100.000000%]
const=0x2bc830b2 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x2bc830b2 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x2bc830b2 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x2bc830b2 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x2bc830b2 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x2bc830b2 G: total=2831622 pr(0)=627781[22.170367%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1643[0.058023%]
const=0x2bc830b2 H: total=347707 pr(0)=58591[16.850682%] pr(2^-30)=289116[83.149318%]
const=0x2bc830b2 I: total=610683 pr(0)=220447[36.098434%] pr(2^-30)=389565[63.791689%] pr(2^-25)=671[0.109877%]
const=0x2bc830b2 J: total=455916 pr(0)=71673[15.720659%] pr(2^-30)=384039[84.234596%] pr(2^-25)=180[0.039481%] pr(2^-20)=24[0.005264%]
const=0x2bc830b2 K: total=5813139 pr(0)=4345033[74.745039%] pr(2^-30)=1468014[25.253379%] pr(2^-25)=92[0.001583%]
const=0x2bc830b2 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x2bc830b2 M: total=50713466 pr(0)=7092111[13.984670%] pr(2^-30)=43581044[85.935842%] pr(2^-25)=40012[0.078898%] pr(2^-20)=299[0.000590%]
const=0x2bc830b2 N: total=284708444 pr(0)=22018306[7.733633%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96832[0.034011%]
const=0x2bc830b2 O: total=295744442 pr(0)=22986256[7.772337%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=102168[0.034546%] pr(2^-20)=192[0.000065%]
const=0x2bc830b5 A: total=708111 pr(0)=708111[100.000000%]
const=0x2bc830b5 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x2bc830b5 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x2bc830b5 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x2bc830b5 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x2bc830b5 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x2bc830b5 G: total=2831622 pr(0)=628495[22.195583%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=929[0.032808%]
const=0x2bc830b5 H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x2bc830b5 I: total=610683 pr(0)=220782[36.153291%] pr(2^-30)=389563[63.791361%] pr(2^-25)=332[0.054365%] pr(2^-20)=6[0.000983%]
const=0x2bc830b5 J: total=455916 pr(0)=71682[15.722633%] pr(2^-30)=384038[84.234377%] pr(2^-25)=172[0.037726%] pr(2^-20)=24[0.005264%]
const=0x2bc830b5 K: total=5813139 pr(0)=4345033[74.745039%] pr(2^-30)=1468014[25.253379%] pr(2^-25)=92[0.001583%]
const=0x2bc830b5 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x2bc830b5 M: total=50713466 pr(0)=7092112[13.984672%] pr(2^-30)=43581038[85.935830%] pr(2^-25)=39990[0.078855%] pr(2^-20)=326[0.000643%]
const=0x2bc830b5 N: total=284708444 pr(0)=22017906[7.733492%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=97232[0.034151%]
const=0x2bc830b5 O: total=295744442 pr(0)=22985584[7.772110%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=102840[0.034773%] pr(2^-20)=192[0.000065%]
const=0x2bc830bb A: total=708111 pr(0)=708111[100.000000%]
const=0x2bc830bb B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x2bc830bb C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x2bc830bb D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x2bc830bb E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x2bc830bb F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x2bc830bb G: total=2831622 pr(0)=628478[22.194982%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=946[0.033408%]
const=0x2bc830bb H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x2bc830bb I: total=610683 pr(0)=220753[36.148542%] pr(2^-30)=389565[63.791689%] pr(2^-25)=360[0.058950%] pr(2^-20)=5[0.000819%]
const=0x2bc830bb J: total=455916 pr(0)=71679[15.721975%] pr(2^-30)=384037[84.234157%] pr(2^-25)=176[0.038604%] pr(2^-20)=24[0.005264%]
const=0x2bc830bb K: total=5813139 pr(0)=4345033[74.745039%] pr(2^-30)=1468014[25.253379%] pr(2^-25)=92[0.001583%]
const=0x2bc830bb L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x2bc830bb M: total=50713466 pr(0)=7091995[13.984442%] pr(2^-30)=43581039[85.935832%] pr(2^-25)=40107[0.079086%] pr(2^-20)=325[0.000641%]
const=0x2bc830bb N: total=284708444 pr(0)=22017255[7.733264%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=97883[0.034380%]
const=0x2bc830bb O: total=295744442 pr(0)=22985162[7.771968%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=103262[0.034916%] pr(2^-20)=192[0.000065%]
const=0x2da066c4 A: total=708111 pr(0)=708111[100.000000%]
const=0x2da066c4 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x2da066c4 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x2da066c4 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x2da066c4 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x2da066c4 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x2da066c4 G: total=2831622 pr(0)=628257[22.187178%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1167[0.041213%]
const=0x2da066c4 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x2da066c4 I: total=610683 pr(0)=220700[36.139863%] pr(2^-30)=389567[63.792016%] pr(2^-25)=412[0.067465%] pr(2^-20)=4[0.000655%]
const=0x2da066c4 J: total=455916 pr(0)=71671[15.720220%] pr(2^-30)=384037[84.234157%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0x2da066c4 K: total=5813139 pr(0)=4345034[74.745056%] pr(2^-30)=1468016[25.253413%] pr(2^-25)=89[0.001531%]
const=0x2da066c4 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x2da066c4 M: total=50713466 pr(0)=7092155[13.984757%] pr(2^-30)=43581036[85.935826%] pr(2^-25)=39991[0.078857%] pr(2^-20)=284[0.000560%]
const=0x2da066c4 N: total=284708444 pr(0)=22019123[7.733920%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96015[0.033724%]
const=0x2da066c4 O: total=295744442 pr(0)=22986648[7.772470%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101776[0.034413%] pr(2^-20)=192[0.000065%]
const=0x2dea0845 A: total=708111 pr(0)=708111[100.000000%]
const=0x2dea0845 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x2dea0845 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x2dea0845 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x2dea0845 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x2dea0845 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x2dea0845 G: total=2831622 pr(0)=628199[22.185129%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1225[0.043261%]
const=0x2dea0845 H: total=347707 pr(0)=58591[16.850682%] pr(2^-30)=289116[83.149318%]
const=0x2dea0845 I: total=610683 pr(0)=220653[36.132167%] pr(2^-30)=389565[63.791689%] pr(2^-25)=459[0.075162%] pr(2^-20)=6[0.000983%]
const=0x2dea0845 J: total=455916 pr(0)=71699[15.726362%] pr(2^-30)=384039[84.234596%] pr(2^-25)=154[0.033778%] pr(2^-20)=24[0.005264%]
const=0x2dea0845 K: total=5813139 pr(0)=4345038[74.745125%] pr(2^-30)=1468012[25.253344%] pr(2^-25)=89[0.001531%]
const=0x2dea0845 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x2dea0845 M: total=50713466 pr(0)=7092407[13.985254%] pr(2^-30)=43581051[85.935856%] pr(2^-25)=39707[0.078297%] pr(2^-20)=301[0.000594%]
const=0x2dea0845 N: total=284708444 pr(0)=22018510[7.733705%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96628[0.033939%]
const=0x2dea0845 O: total=295744442 pr(0)=22986508[7.772423%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101916[0.034461%] pr(2^-20)=192[0.000065%]
const=0x2e2f712d A: total=708111 pr(0)=708111[100.000000%]
const=0x2e2f712d B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x2e2f712d C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x2e2f712d D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x2e2f712d E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x2e2f712d F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x2e2f712d G: total=2831622 pr(0)=628478[22.194982%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=946[0.033408%]
const=0x2e2f712d H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x2e2f712d I: total=610683 pr(0)=220727[36.144284%] pr(2^-30)=389565[63.791689%] pr(2^-25)=385[0.063044%] pr(2^-20)=6[0.000983%]
const=0x2e2f712d J: total=455916 pr(0)=71691[15.724607%] pr(2^-30)=384038[84.234377%] pr(2^-25)=163[0.035752%] pr(2^-20)=24[0.005264%]
const=0x2e2f712d K: total=5813139 pr(0)=4345038[74.745125%] pr(2^-30)=1468012[25.253344%] pr(2^-25)=89[0.001531%]
const=0x2e2f712d L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x2e2f712d M: total=50713466 pr(0)=7092383[13.985207%] pr(2^-30)=43581033[85.935820%] pr(2^-25)=39747[0.078376%] pr(2^-20)=303[0.000597%]
const=0x2e2f712d N: total=284708444 pr(0)=22019484[7.734047%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=95654[0.033597%]
const=0x2e2f712d O: total=295744442 pr(0)=22987371[7.772714%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101005[0.034153%] pr(2^-20)=240[0.000081%]
const=0x2ed26663 A: total=708111 pr(0)=708111[100.000000%]
const=0x2ed26663 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x2ed26663 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x2ed26663 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x2ed26663 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x2ed26663 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x2ed26663 G: total=2831622 pr(0)=628699[22.202787%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=725[0.025604%]
const=0x2ed26663 H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x2ed26663 I: total=610683 pr(0)=220870[36.167701%] pr(2^-30)=389564[63.791525%] pr(2^-25)=249[0.040774%]
const=0x2ed26663 J: total=455916 pr(0)=71672[15.720440%] pr(2^-30)=384038[84.234377%] pr(2^-25)=182[0.039920%] pr(2^-20)=24[0.005264%]
const=0x2ed26663 K: total=5813139 pr(0)=4345032[74.745022%] pr(2^-30)=1468015[25.253396%] pr(2^-25)=92[0.001583%]
const=0x2ed26663 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x2ed26663 M: total=50713466 pr(0)=7091467[13.983400%] pr(2^-30)=43581034[85.935822%] pr(2^-25)=40642[0.080140%] pr(2^-20)=323[0.000637%]
const=0x2ed26663 N: total=284708444 pr(0)=22015360[7.732598%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99778[0.035046%]
const=0x2ed26663 O: total=295744442 pr(0)=22983265[7.771326%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105159[0.035557%] pr(2^-20)=192[0.000065%]
const=0x2ed2667f A: total=708111 pr(0)=708111[100.000000%]
const=0x2ed2667f B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x2ed2667f C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x2ed2667f D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x2ed2667f E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x2ed2667f F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x2ed2667f G: total=2831622 pr(0)=628478[22.194982%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=946[0.033408%]
const=0x2ed2667f H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x2ed2667f I: total=610683 pr(0)=220733[36.145267%] pr(2^-30)=389564[63.791525%] pr(2^-25)=374[0.061243%] pr(2^-20)=12[0.001965%]
const=0x2ed2667f J: total=455916 pr(0)=71675[15.721098%] pr(2^-30)=384037[84.234157%] pr(2^-25)=180[0.039481%] pr(2^-20)=24[0.005264%]
const=0x2ed2667f K: total=5813139 pr(0)=4345032[74.745022%] pr(2^-30)=1468015[25.253396%] pr(2^-25)=92[0.001583%]
const=0x2ed2667f L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x2ed2667f M: total=50713466 pr(0)=7091878[13.984211%] pr(2^-30)=43581038[85.935830%] pr(2^-25)=40228[0.079324%] pr(2^-20)=322[0.000635%]
const=0x2ed2667f N: total=284708444 pr(0)=22016995[7.733172%] pr(2^-30)=262593312[92.232358%] pr(2^-25)=98137[0.034469%]
const=0x2ed2667f O: total=295744442 pr(0)=22984895[7.771877%] pr(2^-30)=272655832[92.193054%] pr(2^-25)=103478[0.034989%] pr(2^-20)=237[0.000080%]
const=0x30dd806f A: total=708111 pr(0)=708111[100.000000%]
const=0x30dd806f B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x30dd806f C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x30dd806f D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x30dd806f E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x30dd806f F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x30dd806f G: total=2831622 pr(0)=628348[22.190391%] pr(2^-30)=2202200[77.771680%] pr(2^-25)=1074[0.037929%]
const=0x30dd806f H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x30dd806f I: total=610683 pr(0)=220720[36.143138%] pr(2^-30)=389563[63.791361%] pr(2^-25)=395[0.064682%] pr(2^-20)=5[0.000819%]
const=0x30dd806f J: total=455916 pr(0)=71686[15.723510%] pr(2^-30)=384038[84.234377%] pr(2^-25)=168[0.036849%] pr(2^-20)=24[0.005264%]
const=0x30dd806f K: total=5813139 pr(0)=4345037[74.745108%] pr(2^-30)=1468013[25.253361%] pr(2^-25)=89[0.001531%]
const=0x30dd806f L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x30dd806f M: total=50713466 pr(0)=7091673[13.983807%] pr(2^-30)=43581039[85.935832%] pr(2^-25)=40475[0.079811%] pr(2^-20)=279[0.000550%]
const=0x30dd806f N: total=284708444 pr(0)=22015360[7.732598%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99778[0.035046%]
const=0x30dd806f O: total=295744442 pr(0)=22983265[7.771326%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105159[0.035557%] pr(2^-20)=192[0.000065%]
const=0x3121cb6b A: total=708111 pr(0)=708111[100.000000%]
const=0x3121cb6b B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3121cb6b C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3121cb6b D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3121cb6b E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3121cb6b F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3121cb6b G: total=2831622 pr(0)=627243[22.151368%] pr(2^-30)=2202206[77.771892%] pr(2^-25)=2173[0.076740%]
const=0x3121cb6b H: total=347707 pr(0)=58591[16.850682%] pr(2^-30)=289116[83.149318%]
const=0x3121cb6b I: total=610683 pr(0)=220424[36.094668%] pr(2^-30)=389567[63.792016%] pr(2^-25)=689[0.112824%] pr(2^-20)=3[0.000491%]
const=0x3121cb6b J: total=455916 pr(0)=71699[15.726362%] pr(2^-30)=384039[84.234596%] pr(2^-25)=154[0.033778%] pr(2^-20)=24[0.005264%]
const=0x3121cb6b K: total=5813139 pr(0)=4345037[74.745108%] pr(2^-30)=1468013[25.253361%] pr(2^-25)=89[0.001531%]
const=0x3121cb6b L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3121cb6b M: total=50713466 pr(0)=7092410[13.985260%] pr(2^-30)=43581038[85.935830%] pr(2^-25)=39726[0.078334%] pr(2^-20)=292[0.000576%]
const=0x3121cb6b N: total=284708444 pr(0)=22018512[7.733705%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96626[0.033939%]
const=0x3121cb6b O: total=295744442 pr(0)=22986465[7.772408%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101959[0.034475%] pr(2^-20)=192[0.000065%]
const=0x3121cb6d A: total=708111 pr(0)=708111[100.000000%]
const=0x3121cb6d B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3121cb6d C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3121cb6d D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3121cb6d E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3121cb6d F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3121cb6d G: total=2831622 pr(0)=626633[22.129825%] pr(2^-30)=2202206[77.771892%] pr(2^-25)=2783[0.098283%]
const=0x3121cb6d H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x3121cb6d I: total=610683 pr(0)=220156[36.050782%] pr(2^-30)=389567[63.792016%] pr(2^-25)=951[0.155727%] pr(2^-20)=9[0.001474%]
const=0x3121cb6d J: total=455916 pr(0)=71692[15.724827%] pr(2^-30)=384038[84.234377%] pr(2^-25)=162[0.035533%] pr(2^-20)=24[0.005264%]
const=0x3121cb6d K: total=5813139 pr(0)=4345037[74.745108%] pr(2^-30)=1468013[25.253361%] pr(2^-25)=89[0.001531%]
const=0x3121cb6d L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3121cb6d M: total=50713466 pr(0)=7092584[13.985603%] pr(2^-30)=43581035[85.935824%] pr(2^-25)=39550[0.077987%] pr(2^-20)=297[0.000586%]
const=0x3121cb6d N: total=284708444 pr(0)=22019754[7.734142%] pr(2^-30)=262593308[92.232357%] pr(2^-25)=95382[0.033502%]
const=0x3121cb6d O: total=295744442 pr(0)=22987721[7.772833%] pr(2^-30)=272655828[92.193052%] pr(2^-25)=100701[0.034050%] pr(2^-20)=192[0.000065%]
const=0x3121cb77 A: total=708111 pr(0)=708111[100.000000%]
const=0x3121cb77 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3121cb77 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3121cb77 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3121cb77 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3121cb77 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3121cb77 G: total=2831622 pr(0)=627101[22.146353%] pr(2^-30)=2202206[77.771892%] pr(2^-25)=2315[0.081755%]
const=0x3121cb77 H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x3121cb77 I: total=610683 pr(0)=220310[36.076000%] pr(2^-30)=389566[63.791853%] pr(2^-25)=798[0.130673%] pr(2^-20)=9[0.001474%]
const=0x3121cb77 J: total=455916 pr(0)=71696[15.725704%] pr(2^-30)=384038[84.234377%] pr(2^-25)=158[0.034656%] pr(2^-20)=24[0.005264%]
const=0x3121cb77 K: total=5813139 pr(0)=4345037[74.745108%] pr(2^-30)=1468013[25.253361%] pr(2^-25)=89[0.001531%]
const=0x3121cb77 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3121cb77 M: total=50713466 pr(0)=7092501[13.985439%] pr(2^-30)=43581032[85.935818%] pr(2^-25)=39636[0.078157%] pr(2^-20)=297[0.000586%]
const=0x3121cb77 N: total=284708444 pr(0)=22019123[7.733920%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96015[0.033724%]
const=0x3121cb77 O: total=295744442 pr(0)=22986648[7.772470%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101776[0.034413%] pr(2^-20)=192[0.000065%]
const=0x316ba5e8 A: total=708111 pr(0)=708111[100.000000%]
const=0x316ba5e8 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x316ba5e8 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x316ba5e8 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x316ba5e8 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x316ba5e8 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x316ba5e8 G: total=2831622 pr(0)=628516[22.196324%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=908[0.032066%]
const=0x316ba5e8 H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x316ba5e8 I: total=610683 pr(0)=220691[36.138389%] pr(2^-30)=389564[63.791525%] pr(2^-25)=423[0.069267%] pr(2^-20)=5[0.000819%]
const=0x316ba5e8 J: total=455916 pr(0)=71666[15.719124%] pr(2^-30)=384038[84.234377%] pr(2^-25)=188[0.041236%] pr(2^-20)=24[0.005264%]
const=0x316ba5e8 K: total=5813139 pr(0)=4345037[74.745108%] pr(2^-30)=1468013[25.253361%] pr(2^-25)=89[0.001531%]
const=0x316ba5e8 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x316ba5e8 M: total=50713466 pr(0)=7092064[13.984578%] pr(2^-30)=43581025[85.935805%] pr(2^-25)=40108[0.079087%] pr(2^-20)=269[0.000530%]
const=0x316ba5e8 N: total=284708444 pr(0)=22018512[7.733705%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96626[0.033939%]
const=0x316ba5e8 O: total=295744442 pr(0)=22986465[7.772408%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101959[0.034475%] pr(2^-20)=192[0.000065%]
const=0x316ba5ef A: total=708111 pr(0)=708111[100.000000%]
const=0x316ba5ef B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x316ba5ef C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x316ba5ef D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x316ba5ef E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x316ba5ef F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x316ba5ef G: total=2831622 pr(0)=628413[22.192687%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1011[0.035704%]
const=0x316ba5ef H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x316ba5ef I: total=610683 pr(0)=220669[36.134787%] pr(2^-30)=389564[63.791525%] pr(2^-25)=448[0.073360%] pr(2^-20)=2[0.000328%]
const=0x316ba5ef J: total=455916 pr(0)=71665[15.718904%] pr(2^-30)=384038[84.234377%] pr(2^-25)=189[0.041455%] pr(2^-20)=24[0.005264%]
const=0x316ba5ef K: total=5813139 pr(0)=4345037[74.745108%] pr(2^-30)=1468013[25.253361%] pr(2^-25)=89[0.001531%]
const=0x316ba5ef L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x316ba5ef M: total=50713466 pr(0)=7091964[13.984380%] pr(2^-30)=43581028[85.935810%] pr(2^-25)=40192[0.079253%] pr(2^-20)=282[0.000556%]
const=0x316ba5ef N: total=284708444 pr(0)=22017906[7.733492%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=97232[0.034151%]
const=0x316ba5ef O: total=295744442 pr(0)=22985584[7.772110%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=102840[0.034773%] pr(2^-20)=192[0.000065%]
const=0x316ba5fb A: total=708111 pr(0)=708111[100.000000%]
const=0x316ba5fb B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x316ba5fb C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x316ba5fb D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x316ba5fb E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x316ba5fb F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x316ba5fb G: total=2831622 pr(0)=627858[22.173087%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1566[0.055304%]
const=0x316ba5fb H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x316ba5fb I: total=610683 pr(0)=220335[36.080094%] pr(2^-30)=389565[63.791689%] pr(2^-25)=776[0.127071%] pr(2^-20)=7[0.001146%]
const=0x316ba5fb J: total=455916 pr(0)=71653[15.716272%] pr(2^-30)=384038[84.234377%] pr(2^-25)=197[0.043210%] pr(2^-20)=28[0.006141%]
const=0x316ba5fb K: total=5813139 pr(0)=4345037[74.745108%] pr(2^-30)=1468013[25.253361%] pr(2^-25)=89[0.001531%]
const=0x316ba5fb L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x316ba5fb M: total=50713466 pr(0)=7091417[13.983302%] pr(2^-30)=43581027[85.935808%] pr(2^-25)=40730[0.080314%] pr(2^-20)=292[0.000576%]
const=0x316ba5fb N: total=284708444 pr(0)=22018510[7.733705%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96628[0.033939%]
const=0x316ba5fb O: total=295744442 pr(0)=22986508[7.772423%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101916[0.034461%] pr(2^-20)=192[0.000065%]
const=0x316ba5ff A: total=708111 pr(0)=708111[100.000000%]
const=0x316ba5ff B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x316ba5ff C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x316ba5ff D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x316ba5ff E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x316ba5ff F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x316ba5ff G: total=2831622 pr(0)=628866[22.208685%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=558[0.019706%]
const=0x316ba5ff H: total=347707 pr(0)=58591[16.850682%] pr(2^-30)=289116[83.149318%]
const=0x316ba5ff I: total=610683 pr(0)=220800[36.156238%] pr(2^-30)=389565[63.791689%] pr(2^-25)=311[0.050927%] pr(2^-20)=7[0.001146%]
const=0x316ba5ff J: total=455916 pr(0)=71669[15.719782%] pr(2^-30)=384039[84.234596%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0x316ba5ff K: total=5813139 pr(0)=4345037[74.745108%] pr(2^-30)=1468013[25.253361%] pr(2^-25)=89[0.001531%]
const=0x316ba5ff L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x316ba5ff M: total=50713466 pr(0)=7092166[13.984779%] pr(2^-30)=43581029[85.935812%] pr(2^-25)=39987[0.078849%] pr(2^-20)=284[0.000560%]
const=0x316ba5ff N: total=284708444 pr(0)=22019123[7.733920%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96015[0.033724%]
const=0x316ba5ff O: total=295744442 pr(0)=22986648[7.772470%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101776[0.034413%] pr(2^-20)=192[0.000065%]
const=0x3219a544 A: total=708111 pr(0)=708111[100.000000%]
const=0x3219a544 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3219a544 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3219a544 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3219a544 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3219a544 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3219a544 G: total=2831622 pr(0)=628606[22.199503%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=818[0.028888%]
const=0x3219a544 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x3219a544 I: total=610683 pr(0)=220720[36.143138%] pr(2^-30)=389565[63.791689%] pr(2^-25)=390[0.063863%] pr(2^-20)=8[0.001310%]
const=0x3219a544 J: total=455916 pr(0)=71675[15.721098%] pr(2^-30)=384037[84.234157%] pr(2^-25)=180[0.039481%] pr(2^-20)=24[0.005264%]
const=0x3219a544 K: total=5813139 pr(0)=4345030[74.744987%] pr(2^-30)=1468016[25.253413%] pr(2^-25)=93[0.001600%]
const=0x3219a544 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3219a544 M: total=50713466 pr(0)=7091880[13.984215%] pr(2^-30)=43581038[85.935830%] pr(2^-25)=40226[0.079320%] pr(2^-20)=322[0.000635%]
const=0x3219a544 N: total=284708444 pr(0)=22016995[7.733172%] pr(2^-30)=262593312[92.232358%] pr(2^-25)=98137[0.034469%]
const=0x3219a544 O: total=295744442 pr(0)=22984895[7.771877%] pr(2^-30)=272655832[92.193054%] pr(2^-25)=103478[0.034989%] pr(2^-20)=237[0.000080%]
const=0x3219a54b A: total=708111 pr(0)=708111[100.000000%]
const=0x3219a54b B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3219a54b C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3219a54b D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3219a54b E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3219a54b F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3219a54b G: total=2831622 pr(0)=628459[22.194311%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=965[0.034079%]
const=0x3219a54b H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x3219a54b I: total=610683 pr(0)=220749[36.147887%] pr(2^-30)=389564[63.791525%] pr(2^-25)=367[0.060097%] pr(2^-20)=3[0.000491%]
const=0x3219a54b J: total=455916 pr(0)=71683[15.722852%] pr(2^-30)=384037[84.234157%] pr(2^-25)=172[0.037726%] pr(2^-20)=24[0.005264%]
const=0x3219a54b K: total=5813139 pr(0)=4345030[74.744987%] pr(2^-30)=1468016[25.253413%] pr(2^-25)=93[0.001600%]
const=0x3219a54b L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3219a54b M: total=50713466 pr(0)=7092111[13.984670%] pr(2^-30)=43581039[85.935832%] pr(2^-25)=39990[0.078855%] pr(2^-20)=326[0.000643%]
const=0x3219a54b N: total=284708444 pr(0)=22017906[7.733492%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=97232[0.034151%]
const=0x3219a54b O: total=295744442 pr(0)=22985584[7.772110%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=102840[0.034773%] pr(2^-20)=192[0.000065%]
const=0x3219a55f A: total=708111 pr(0)=708111[100.000000%]
const=0x3219a55f B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3219a55f C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3219a55f D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3219a55f E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3219a55f F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3219a55f G: total=2831622 pr(0)=628482[22.195124%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=942[0.033267%]
const=0x3219a55f H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x3219a55f I: total=610683 pr(0)=220709[36.141337%] pr(2^-30)=389564[63.791525%] pr(2^-25)=405[0.066319%] pr(2^-20)=5[0.000819%]
const=0x3219a55f J: total=455916 pr(0)=71674[15.720878%] pr(2^-30)=384037[84.234157%] pr(2^-25)=181[0.039700%] pr(2^-20)=24[0.005264%]
const=0x3219a55f K: total=5813139 pr(0)=4345030[74.744987%] pr(2^-30)=1468016[25.253413%] pr(2^-25)=93[0.001600%]
const=0x3219a55f L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3219a55f M: total=50713466 pr(0)=7092298[13.985039%] pr(2^-30)=43581034[85.935822%] pr(2^-25)=39813[0.078506%] pr(2^-20)=321[0.000633%]
const=0x3219a55f N: total=284708444 pr(0)=22019123[7.733920%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96015[0.033724%]
const=0x3219a55f O: total=295744442 pr(0)=22986648[7.772470%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101776[0.034413%] pr(2^-20)=192[0.000065%]
const=0x32e4b216 A: total=708111 pr(0)=708111[100.000000%]
const=0x32e4b216 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x32e4b216 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x32e4b216 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x32e4b216 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x32e4b216 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x32e4b216 G: total=2831622 pr(0)=628565[22.198055%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=859[0.030336%]
const=0x32e4b216 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x32e4b216 I: total=610683 pr(0)=220873[36.168192%] pr(2^-30)=389564[63.791525%] pr(2^-25)=243[0.039792%] pr(2^-20)=3[0.000491%]
const=0x32e4b216 J: total=455916 pr(0)=71692[15.724827%] pr(2^-30)=384037[84.234157%] pr(2^-25)=163[0.035752%] pr(2^-20)=24[0.005264%]
const=0x32e4b216 K: total=5813139 pr(0)=4345040[74.745159%] pr(2^-30)=1468010[25.253310%] pr(2^-25)=89[0.001531%]
const=0x32e4b216 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x32e4b216 M: total=50713466 pr(0)=7092381[13.985203%] pr(2^-30)=43581035[85.935824%] pr(2^-25)=39747[0.078376%] pr(2^-20)=303[0.000597%]
const=0x32e4b216 N: total=284708444 pr(0)=22019484[7.734047%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=95654[0.033597%]
const=0x32e4b216 O: total=295744442 pr(0)=22987371[7.772714%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101005[0.034153%] pr(2^-20)=240[0.000081%]
const=0x343b9da8 A: total=708111 pr(0)=708111[100.000000%]
const=0x343b9da8 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x343b9da8 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x343b9da8 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x343b9da8 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x343b9da8 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x343b9da8 G: total=2831622 pr(0)=628504[22.195900%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=920[0.032490%]
const=0x343b9da8 H: total=347707 pr(0)=58591[16.850682%] pr(2^-30)=289116[83.149318%]
const=0x343b9da8 I: total=610683 pr(0)=220689[36.138062%] pr(2^-30)=389564[63.791525%] pr(2^-25)=424[0.069430%] pr(2^-20)=6[0.000983%]
const=0x343b9da8 J: total=455916 pr(0)=71691[15.724607%] pr(2^-30)=384039[84.234596%] pr(2^-25)=162[0.035533%] pr(2^-20)=24[0.005264%]
const=0x343b9da8 K: total=5813139 pr(0)=4345035[74.745073%] pr(2^-30)=1468015[25.253396%] pr(2^-25)=89[0.001531%]
const=0x343b9da8 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x343b9da8 M: total=50713466 pr(0)=7092569[13.985573%] pr(2^-30)=43581045[85.935844%] pr(2^-25)=39555[0.077997%] pr(2^-20)=297[0.000586%]
const=0x343b9da8 N: total=284708444 pr(0)=22019754[7.734142%] pr(2^-30)=262593308[92.232357%] pr(2^-25)=95382[0.033502%]
const=0x343b9da8 O: total=295744442 pr(0)=22987721[7.772833%] pr(2^-30)=272655828[92.193052%] pr(2^-25)=100701[0.034050%] pr(2^-20)=192[0.000065%]
const=0x3471f327 A: total=708111 pr(0)=708111[100.000000%]
const=0x3471f327 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3471f327 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3471f327 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3471f327 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3471f327 F: total=5135 pr(0)=3639[70.866602%] pr(2^-30)=1496[29.133398%]
const=0x3471f327 G: total=2831622 pr(0)=628139[22.183010%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1285[0.045380%]
const=0x3471f327 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x3471f327 I: total=610683 pr(0)=220587[36.121359%] pr(2^-30)=389567[63.792016%] pr(2^-25)=523[0.085642%] pr(2^-20)=6[0.000983%]
const=0x3471f327 J: total=455916 pr(0)=71671[15.720220%] pr(2^-30)=384037[84.234157%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0x3471f327 K: total=5813139 pr(0)=4345040[74.745159%] pr(2^-30)=1468010[25.253310%] pr(2^-25)=89[0.001531%]
const=0x3471f327 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3471f327 M: total=50713466 pr(0)=7091459[13.983385%] pr(2^-30)=43581028[85.935810%] pr(2^-25)=40694[0.080243%] pr(2^-20)=285[0.000562%]
const=0x3471f327 N: total=284708444 pr(0)=22015347[7.732594%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99791[0.035050%]
const=0x3471f327 O: total=295744442 pr(0)=22983309[7.771341%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105115[0.035543%] pr(2^-20)=192[0.000065%]
const=0x35c7d6b9 A: total=708111 pr(0)=708111[100.000000%]
const=0x35c7d6b9 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x35c7d6b9 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x35c7d6b9 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x35c7d6b9 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x35c7d6b9 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x35c7d6b9 G: total=2831622 pr(0)=628194[22.184953%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1230[0.043438%]
const=0x35c7d6b9 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x35c7d6b9 I: total=610683 pr(0)=220598[36.123160%] pr(2^-30)=389564[63.791525%] pr(2^-25)=518[0.084823%] pr(2^-20)=3[0.000491%]
const=0x35c7d6b9 J: total=455916 pr(0)=71687[15.723730%] pr(2^-30)=384037[84.234157%] pr(2^-25)=168[0.036849%] pr(2^-20)=24[0.005264%]
const=0x35c7d6b9 K: total=5813139 pr(0)=4345038[74.745125%] pr(2^-30)=1468012[25.253344%] pr(2^-25)=89[0.001531%]
const=0x35c7d6b9 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x35c7d6b9 M: total=50713466 pr(0)=7091878[13.984211%] pr(2^-30)=43581034[85.935822%] pr(2^-25)=40275[0.079417%] pr(2^-20)=279[0.000550%]
const=0x35c7d6b9 N: total=284708444 pr(0)=22015347[7.732594%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99791[0.035050%]
const=0x35c7d6b9 O: total=295744442 pr(0)=22983309[7.771341%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105115[0.035543%] pr(2^-20)=192[0.000065%]
const=0x3703f380 A: total=708111 pr(0)=708111[100.000000%]
const=0x3703f380 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3703f380 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3703f380 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3703f380 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3703f380 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3703f380 G: total=2831622 pr(0)=628350[22.190462%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1074[0.037929%]
const=0x3703f380 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x3703f380 I: total=610683 pr(0)=220675[36.135769%] pr(2^-30)=389564[63.791525%] pr(2^-25)=441[0.072214%] pr(2^-20)=3[0.000491%]
const=0x3703f380 J: total=455916 pr(0)=71679[15.721975%] pr(2^-30)=384037[84.234157%] pr(2^-25)=176[0.038604%] pr(2^-20)=24[0.005264%]
const=0x3703f380 K: total=5813139 pr(0)=4345040[74.745159%] pr(2^-30)=1468010[25.253310%] pr(2^-25)=89[0.001531%]
const=0x3703f380 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3703f380 M: total=50713466 pr(0)=7091998[13.984447%] pr(2^-30)=43581036[85.935826%] pr(2^-25)=40107[0.079086%] pr(2^-20)=325[0.000641%]
const=0x3703f380 N: total=284708444 pr(0)=22017255[7.733264%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=97883[0.034380%]
const=0x3703f380 O: total=295744442 pr(0)=22985162[7.771968%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=103262[0.034916%] pr(2^-20)=192[0.000065%]
const=0x3703f39a A: total=708111 pr(0)=708111[100.000000%]
const=0x3703f39a B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3703f39a C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3703f39a D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3703f39a E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3703f39a F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3703f39a G: total=2831622 pr(0)=627929[22.175594%] pr(2^-30)=2202200[77.771680%] pr(2^-25)=1493[0.052726%]
const=0x3703f39a H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x3703f39a I: total=610683 pr(0)=220446[36.098270%] pr(2^-30)=389564[63.791525%] pr(2^-25)=670[0.109713%] pr(2^-20)=3[0.000491%]
const=0x3703f39a J: total=455916 pr(0)=71674[15.720878%] pr(2^-30)=384037[84.234157%] pr(2^-25)=181[0.039700%] pr(2^-20)=24[0.005264%]
const=0x3703f39a K: total=5813139 pr(0)=4345040[74.745159%] pr(2^-30)=1468010[25.253310%] pr(2^-25)=89[0.001531%]
const=0x3703f39a L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3703f39a M: total=50713466 pr(0)=7092297[13.985037%] pr(2^-30)=43581033[85.935820%] pr(2^-25)=39815[0.078510%] pr(2^-20)=321[0.000633%]
const=0x3703f39a N: total=284708444 pr(0)=22019123[7.733920%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96015[0.033724%]
const=0x3703f39a O: total=295744442 pr(0)=22986648[7.772470%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101776[0.034413%] pr(2^-20)=192[0.000065%]
const=0x3703f39b A: total=708111 pr(0)=708111[100.000000%]
const=0x3703f39b B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3703f39b C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3703f39b D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3703f39b E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3703f39b F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3703f39b G: total=2831622 pr(0)=628105[22.181810%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1319[0.046581%]
const=0x3703f39b H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x3703f39b I: total=610683 pr(0)=220476[36.103183%] pr(2^-30)=389564[63.791525%] pr(2^-25)=635[0.103982%] pr(2^-20)=8[0.001310%]
const=0x3703f39b J: total=455916 pr(0)=71673[15.720659%] pr(2^-30)=384037[84.234157%] pr(2^-25)=182[0.039920%] pr(2^-20)=24[0.005264%]
const=0x3703f39b K: total=5813139 pr(0)=4345040[74.745159%] pr(2^-30)=1468010[25.253310%] pr(2^-25)=89[0.001531%]
const=0x3703f39b L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3703f39b M: total=50713466 pr(0)=7092301[13.985045%] pr(2^-30)=43581030[85.935814%] pr(2^-25)=39809[0.078498%] pr(2^-20)=326[0.000643%]
const=0x3703f39b N: total=284708444 pr(0)=22019754[7.734142%] pr(2^-30)=262593308[92.232357%] pr(2^-25)=95382[0.033502%]
const=0x3703f39b O: total=295744442 pr(0)=22987721[7.772833%] pr(2^-30)=272655828[92.193052%] pr(2^-25)=100701[0.034050%] pr(2^-20)=192[0.000065%]
const=0x37b48a58 A: total=708111 pr(0)=708111[100.000000%]
const=0x37b48a58 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x37b48a58 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x37b48a58 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x37b48a58 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x37b48a58 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x37b48a58 G: total=2831622 pr(0)=627952[22.176406%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1472[0.051984%]
const=0x37b48a58 H: total=347707 pr(0)=58590[16.850394%] pr(2^-30)=289117[83.149606%]
const=0x37b48a58 I: total=610683 pr(0)=220452[36.099253%] pr(2^-30)=389565[63.791689%] pr(2^-25)=653[0.106929%] pr(2^-20)=13[0.002129%]
const=0x37b48a58 J: total=455916 pr(0)=71664[15.718685%] pr(2^-30)=384040[84.234815%] pr(2^-25)=188[0.041236%] pr(2^-20)=24[0.005264%]
const=0x37b48a58 K: total=5813139 pr(0)=4345039[74.745142%] pr(2^-30)=1468011[25.253327%] pr(2^-25)=89[0.001531%]
const=0x37b48a58 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x37b48a58 M: total=50713466 pr(0)=7091961[13.984374%] pr(2^-30)=43581039[85.935832%] pr(2^-25)=40182[0.079233%] pr(2^-20)=284[0.000560%]
const=0x37b48a58 N: total=284708444 pr(0)=22018920[7.733849%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96218[0.033795%]
const=0x37b48a58 O: total=295744442 pr(0)=22986909[7.772558%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101515[0.034325%] pr(2^-20)=192[0.000065%]
const=0x39db2945 A: total=708111 pr(0)=708111[100.000000%]
const=0x39db2945 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x39db2945 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x39db2945 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x39db2945 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x39db2945 F: total=5135 pr(0)=3639[70.866602%] pr(2^-30)=1496[29.133398%]
const=0x39db2945 G: total=2831622 pr(0)=628194[22.184953%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1230[0.043438%]
const=0x39db2945 H: total=347707 pr(0)=58591[16.850682%] pr(2^-30)=289116[83.149318%]
const=0x39db2945 I: total=610683 pr(0)=220582[36.120540%] pr(2^-30)=389568[63.792180%] pr(2^-25)=527[0.086297%] pr(2^-20)=6[0.000983%]
const=0x39db2945 J: total=455916 pr(0)=71664[15.718685%] pr(2^-30)=384039[84.234596%] pr(2^-25)=189[0.041455%] pr(2^-20)=24[0.005264%]
const=0x39db2945 K: total=5813139 pr(0)=4345028[74.744953%] pr(2^-30)=1468018[25.253447%] pr(2^-25)=93[0.001600%]
const=0x39db2945 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x39db2945 M: total=50713466 pr(0)=7091959[13.984371%] pr(2^-30)=43581033[85.935820%] pr(2^-25)=40192[0.079253%] pr(2^-20)=282[0.000556%]
const=0x39db2945 N: total=284708444 pr(0)=22017906[7.733492%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=97232[0.034151%]
const=0x39db2945 O: total=295744442 pr(0)=22985584[7.772110%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=102840[0.034773%] pr(2^-20)=192[0.000065%]
const=0x39db2948 A: total=708111 pr(0)=708111[100.000000%]
const=0x39db2948 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x39db2948 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x39db2948 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x39db2948 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x39db2948 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x39db2948 G: total=2831622 pr(0)=628350[22.190462%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1074[0.037929%]
const=0x39db2948 H: total=347707 pr(0)=58591[16.850682%] pr(2^-30)=289116[83.149318%]
const=0x39db2948 I: total=610683 pr(0)=220675[36.135769%] pr(2^-30)=389564[63.791525%] pr(2^-25)=440[0.072050%] pr(2^-20)=4[0.000655%]
const=0x39db2948 J: total=455916 pr(0)=71669[15.719782%] pr(2^-30)=384039[84.234596%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0x39db2948 K: total=5813139 pr(0)=4345028[74.744953%] pr(2^-30)=1468018[25.253447%] pr(2^-25)=93[0.001600%]
const=0x39db2948 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x39db2948 M: total=50713466 pr(0)=7091450[13.983367%] pr(2^-30)=43581035[85.935824%] pr(2^-25)=40696[0.080247%] pr(2^-20)=285[0.000562%]
const=0x39db2948 N: total=284708444 pr(0)=22015347[7.732594%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99791[0.035050%]
const=0x39db2948 O: total=295744442 pr(0)=22983309[7.771341%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105115[0.035543%] pr(2^-20)=192[0.000065%]
const=0x39db2955 A: total=708111 pr(0)=708111[100.000000%]
const=0x39db2955 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x39db2955 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x39db2955 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x39db2955 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x39db2955 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x39db2955 G: total=2831622 pr(0)=628199[22.185129%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1225[0.043261%]
const=0x39db2955 H: total=347707 pr(0)=58591[16.850682%] pr(2^-30)=289116[83.149318%]
const=0x39db2955 I: total=610683 pr(0)=220605[36.124307%] pr(2^-30)=389563[63.791361%] pr(2^-25)=514[0.084168%] pr(2^-20)=1[0.000164%]
const=0x39db2955 J: total=455916 pr(0)=71669[15.719782%] pr(2^-30)=384039[84.234596%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0x39db2955 K: total=5813139 pr(0)=4345028[74.744953%] pr(2^-30)=1468018[25.253447%] pr(2^-25)=93[0.001600%]
const=0x39db2955 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x39db2955 M: total=50713466 pr(0)=7092163[13.984773%] pr(2^-30)=43581033[85.935820%] pr(2^-25)=39986[0.078847%] pr(2^-20)=284[0.000560%]
const=0x39db2955 N: total=284708444 pr(0)=22019123[7.733920%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96015[0.033724%]
const=0x39db2955 O: total=295744442 pr(0)=22986648[7.772470%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101776[0.034413%] pr(2^-20)=192[0.000065%]
const=0x39db2957 A: total=708111 pr(0)=708111[100.000000%]
const=0x39db2957 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x39db2957 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x39db2957 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x39db2957 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x39db2957 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x39db2957 G: total=2831622 pr(0)=628130[22.182692%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1294[0.045698%]
const=0x39db2957 H: total=347707 pr(0)=58591[16.850682%] pr(2^-30)=289116[83.149318%]
const=0x39db2957 I: total=610683 pr(0)=220536[36.113008%] pr(2^-30)=389563[63.791361%] pr(2^-25)=577[0.094484%] pr(2^-20)=7[0.001146%]
const=0x39db2957 J: total=455916 pr(0)=71669[15.719782%] pr(2^-30)=384039[84.234596%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0x39db2957 K: total=5813139 pr(0)=4345028[74.744953%] pr(2^-30)=1468018[25.253447%] pr(2^-25)=93[0.001600%]
const=0x39db2957 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x39db2957 M: total=50713466 pr(0)=7091922[13.984298%] pr(2^-30)=43581038[85.935830%] pr(2^-25)=40215[0.079298%] pr(2^-20)=291[0.000574%]
const=0x39db2957 N: total=284708444 pr(0)=22018812[7.733811%] pr(2^-30)=262593314[92.232359%] pr(2^-25)=96318[0.033830%]
const=0x39db2957 O: total=295744442 pr(0)=22986810[7.772525%] pr(2^-30)=272655834[92.193054%] pr(2^-25)=101606[0.034356%] pr(2^-20)=192[0.000065%]
const=0x3a1e5021 A: total=708111 pr(0)=708111[100.000000%]
const=0x3a1e5021 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3a1e5021 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3a1e5021 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3a1e5021 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3a1e5021 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3a1e5021 G: total=2831622 pr(0)=628453[22.194099%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=971[0.034291%]
const=0x3a1e5021 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x3a1e5021 I: total=610683 pr(0)=220718[36.142811%] pr(2^-30)=389568[63.792180%] pr(2^-25)=390[0.063863%] pr(2^-20)=7[0.001146%]
const=0x3a1e5021 J: total=455916 pr(0)=71671[15.720220%] pr(2^-30)=384037[84.234157%] pr(2^-25)=184[0.040358%] pr(2^-20)=24[0.005264%]
const=0x3a1e5021 K: total=5813139 pr(0)=4345041[74.745176%] pr(2^-30)=1468009[25.253293%] pr(2^-25)=89[0.001531%]
const=0x3a1e5021 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3a1e5021 M: total=50713466 pr(0)=7091942[13.984337%] pr(2^-30)=43581021[85.935797%] pr(2^-25)=40212[0.079293%] pr(2^-20)=291[0.000574%]
const=0x3a1e5021 N: total=284708444 pr(0)=22018812[7.733811%] pr(2^-30)=262593314[92.232359%] pr(2^-25)=96318[0.033830%]
const=0x3a1e5021 O: total=295744442 pr(0)=22986810[7.772525%] pr(2^-30)=272655834[92.193054%] pr(2^-25)=101606[0.034356%] pr(2^-20)=192[0.000065%]
const=0x3f4e6867 A: total=708111 pr(0)=708111[100.000000%]
const=0x3f4e6867 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3f4e6867 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3f4e6867 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3f4e6867 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3f4e6867 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3f4e6867 G: total=2831622 pr(0)=628866[22.208685%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=558[0.019706%]
const=0x3f4e6867 H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x3f4e6867 I: total=610683 pr(0)=220836[36.162133%] pr(2^-30)=389563[63.791361%] pr(2^-25)=284[0.046505%]
const=0x3f4e6867 J: total=455916 pr(0)=71701[15.726801%] pr(2^-30)=384037[84.234157%] pr(2^-25)=154[0.033778%] pr(2^-20)=24[0.005264%]
const=0x3f4e6867 K: total=5813139 pr(0)=4345037[74.745108%] pr(2^-30)=1468012[25.253344%] pr(2^-25)=90[0.001548%]
const=0x3f4e6867 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3f4e6867 M: total=50713466 pr(0)=7092430[13.985299%] pr(2^-30)=43581032[85.935818%] pr(2^-25)=39703[0.078289%] pr(2^-20)=301[0.000594%]
const=0x3f4e6867 N: total=284708444 pr(0)=22018510[7.733705%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96628[0.033939%]
const=0x3f4e6867 O: total=295744442 pr(0)=22986508[7.772423%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101916[0.034461%] pr(2^-20)=192[0.000065%]
const=0x3f4e687a A: total=708111 pr(0)=708111[100.000000%]
const=0x3f4e687a B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3f4e687a C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3f4e687a D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3f4e687a E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3f4e687a F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3f4e687a G: total=2831622 pr(0)=628455[22.194170%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=969[0.034221%]
const=0x3f4e687a H: total=347707 pr(0)=58593[16.851257%] pr(2^-30)=289114[83.148743%]
const=0x3f4e687a I: total=610683 pr(0)=220655[36.132494%] pr(2^-30)=389566[63.791853%] pr(2^-25)=462[0.075653%]
const=0x3f4e687a J: total=455916 pr(0)=71696[15.725704%] pr(2^-30)=384037[84.234157%] pr(2^-25)=159[0.034875%] pr(2^-20)=24[0.005264%]
const=0x3f4e687a K: total=5813139 pr(0)=4345037[74.745108%] pr(2^-30)=1468012[25.253344%] pr(2^-25)=90[0.001548%]
const=0x3f4e687a L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3f4e687a M: total=50713466 pr(0)=7091587[13.983637%] pr(2^-30)=43581032[85.935818%] pr(2^-25)=40546[0.079951%] pr(2^-20)=301[0.000594%]
const=0x3f4e687a N: total=284708444 pr(0)=22015360[7.732598%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=99778[0.035046%]
const=0x3f4e687a O: total=295744442 pr(0)=22983265[7.771326%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=105159[0.035557%] pr(2^-20)=192[0.000065%]
const=0x3fb37f23 A: total=708111 pr(0)=708111[100.000000%]
const=0x3fb37f23 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3fb37f23 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3fb37f23 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3fb37f23 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3fb37f23 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3fb37f23 G: total=2831622 pr(0)=628738[22.204164%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=686[0.024226%]
const=0x3fb37f23 H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x3fb37f23 I: total=610683 pr(0)=220756[36.149033%] pr(2^-30)=389566[63.791853%] pr(2^-25)=355[0.058132%] pr(2^-20)=6[0.000983%]
const=0x3fb37f23 J: total=455916 pr(0)=71674[15.720878%] pr(2^-30)=384038[84.234377%] pr(2^-25)=180[0.039481%] pr(2^-20)=24[0.005264%]
const=0x3fb37f23 K: total=5813139 pr(0)=4345037[74.745108%] pr(2^-30)=1468013[25.253361%] pr(2^-25)=89[0.001531%]
const=0x3fb37f23 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3fb37f23 M: total=50713466 pr(0)=7092120[13.984688%] pr(2^-30)=43581032[85.935818%] pr(2^-25)=40015[0.078904%] pr(2^-20)=299[0.000590%]
const=0x3fb37f23 N: total=284708444 pr(0)=22018306[7.733633%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96832[0.034011%]
const=0x3fb37f23 O: total=295744442 pr(0)=22986256[7.772337%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=102168[0.034546%] pr(2^-20)=192[0.000065%]
const=0x3fb37f2a A: total=708111 pr(0)=708111[100.000000%]
const=0x3fb37f2a B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3fb37f2a C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3fb37f2a D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3fb37f2a E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3fb37f2a F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3fb37f2a G: total=2831622 pr(0)=627988[22.177678%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=1436[0.050713%]
const=0x3fb37f2a H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x3fb37f2a I: total=610683 pr(0)=220485[36.104657%] pr(2^-30)=389568[63.792180%] pr(2^-25)=627[0.102672%] pr(2^-20)=3[0.000491%]
const=0x3fb37f2a J: total=455916 pr(0)=71678[15.721756%] pr(2^-30)=384038[84.234377%] pr(2^-25)=176[0.038604%] pr(2^-20)=24[0.005264%]
const=0x3fb37f2a K: total=5813139 pr(0)=4345037[74.745108%] pr(2^-30)=1468013[25.253361%] pr(2^-25)=89[0.001531%]
const=0x3fb37f2a L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3fb37f2a M: total=50713466 pr(0)=7091997[13.984445%] pr(2^-30)=43581036[85.935826%] pr(2^-25)=40108[0.079087%] pr(2^-20)=325[0.000641%]
const=0x3fb37f2a N: total=284708444 pr(0)=22017255[7.733264%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=97883[0.034380%]
const=0x3fb37f2a O: total=295744442 pr(0)=22985162[7.771968%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=103262[0.034916%] pr(2^-20)=192[0.000065%]
const=0x3fb37f30 A: total=708111 pr(0)=708111[100.000000%]
const=0x3fb37f30 B: total=2343190 pr(0)=180798[7.715892%] pr(2^-30)=2162392[92.284108%]
const=0x3fb37f30 C: total=2373450 pr(0)=184934[7.791780%] pr(2^-30)=2188420[92.204175%] pr(2^-25)=96[0.004045%]
const=0x3fb37f30 D: total=19404 pr(0)=9029[46.531643%] pr(2^-30)=10375[53.468357%]
const=0x3fb37f30 E: total=1976 pr(0)=481[24.342105%] pr(2^-30)=1495[75.657895%]
const=0x3fb37f30 F: total=5135 pr(0)=3640[70.886076%] pr(2^-30)=1495[29.113924%]
const=0x3fb37f30 G: total=2831622 pr(0)=628810[22.206707%] pr(2^-30)=2202198[77.771609%] pr(2^-25)=614[0.021684%]
const=0x3fb37f30 H: total=347707 pr(0)=58592[16.850969%] pr(2^-30)=289115[83.149031%]
const=0x3fb37f30 I: total=610683 pr(0)=220821[36.159677%] pr(2^-30)=389565[63.791689%] pr(2^-25)=291[0.047652%] pr(2^-20)=6[0.000983%]
const=0x3fb37f30 J: total=455916 pr(0)=71673[15.720659%] pr(2^-30)=384038[84.234377%] pr(2^-25)=181[0.039700%] pr(2^-20)=24[0.005264%]
const=0x3fb37f30 K: total=5813139 pr(0)=4345037[74.745108%] pr(2^-30)=1468013[25.253361%] pr(2^-25)=89[0.001531%]
const=0x3fb37f30 L: total=19040076 pr(0)=10692815[56.159518%] pr(2^-30)=8347261[43.840482%]
const=0x3fb37f30 M: total=50713466 pr(0)=7092299[13.985041%] pr(2^-30)=43581030[85.935814%] pr(2^-25)=39816[0.078512%] pr(2^-20)=321[0.000633%]
const=0x3fb37f30 N: total=284708444 pr(0)=22019123[7.733920%] pr(2^-30)=262593306[92.232356%] pr(2^-25)=96015[0.033724%]
const=0x3fb37f30 O: total=295744442 pr(0)=22986648[7.772470%] pr(2^-30)=272655826[92.193052%] pr(2^-25)=101776[0.034413%] pr(2^-20)=192[0.000065%]
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