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1000.cpp
/** Micro Mezz Macro Flation -- Overheated Economy ., Last Update: Jun. 15th 2014 **/ //{
/** Header .. **/ //{
#pragma comment(linker, "/STACK:36777216")
//#pragma GCC optimize ("O2")
#define LOCAL
//#include "testlib.h"
#include <functional>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <numeric>
#include <cstring>
#include <climits>
#include <cassert>
#include <complex>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>
//#include <tr1/unordered_set>
//#include <tr1/unordered_map>
//#include <array>
using namespace std;
#define REP(i, n) for (int i=0;i<n;++i)
#define FOR(i, a, b) for (int i=a;i<b;++i)
#define DWN(i, b, a) for (int i=b-1;i>=a;--i)
#define REP_1(i, n) for (int i=1;i<=n;++i)
#define FOR_1(i, a, b) for (int i=a;i<=b;++i)
#define DWN_1(i, b, a) for (int i=b;i>=a;--i)
#define REP_C(i, n) for (int n____=n,i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=b,i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=a,i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<n;++i)
#define FOR_N(i, a, b) for (i=a;i<b;++i)
#define DWN_N(i, b, a) for (i=b-1;i>=a;--i)
#define REP_1_C(i, n) for (int n____=n,i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=b,i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=a,i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=n;++i)
#define FOR_1_N(i, a, b) for (i=a;i<=b;++i)
#define DWN_1_N(i, b, a) for (i=b;i>=a;--i)
#define REP_C_N(i, n) for (int n____=(i=0,n);i<n____;++i)
#define FOR_C_N(i, a, b) for (int b____=(i=0,b);i<b____;++i)
#define DWN_C_N(i, b, a) for (int a____=(i=b-1,a);i>=a____;--i)
#define REP_1_C_N(i, n) for (int n____=(i=1,n);i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (int b____=(i=a,b);i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (int a____=(i=b,a);i>=a____;--i)
#define ECH(it, A) for (__typeof(A.begin()) it=A.begin(); it != A.end(); ++it)
#define REP_S(i, str) for (char*i=str;*i;++i)
#define REP_L(i, hd, suc) for (int i=hd;i;i=suc[i])
#define REP_G(i, u) REP_L(i,hd[u],suc)
#define REP_SS(x, s) for (int x=s;x;x=(x-1)&s)
#define DO(n) for ( int ____n = n; ____n-->0; )
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)
#define REP_3(i, j, k, n, m, l) REP(i, n) REP(j, m) REP(k, l)
#define REP_3_1(i, j, k, n, m, l) REP_1(i, n) REP_1(j, m) REP_1(k, l)
#define REP_4(i, j, k, ii, n, m, l, nn) REP(i, n) REP(j, m) REP(k, l) REP(ii, nn)
#define REP_4_1(i, j, k, ii, n, m, l, nn) REP_1(i, n) REP_1(j, m) REP_1(k, l) REP_1(ii, nn)
#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define LBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define UBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int((A).size())
#define PB push_back
#define MP(A, B) make_pair(A, B)
#define PTT pair<T, T>
#define Ts *this
#define rTs return Ts
#define fi first
#define se second
#define re real()
#define im imag()
#define Rush for(int ____T=RD(); ____T--;)
#define Display(A, n, m) { \
REP(i, n){ \
REP(j, m-1) cout << A[i][j] << " "; \
cout << A[i][m-1] << endl; \
} \
}
#define Display_1(A, n, m) { \
REP_1(i, n){ \
REP_1(j, m-1) cout << A[i][j] << " "; \
cout << A[i][m] << endl; \
} \
}
typedef long long LL;
//typedef long double DB;
typedef double DB;
typedef unsigned uint;
typedef unsigned long long uLL;
typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VF;
typedef set<int> SI;
typedef set<string> SS;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;
template<class T> inline T& RD(T &);
template<class T> inline void OT(const T &);
//inline int RD(){int x; return RD(x);}
inline LL RD(){LL x; return RD(x);}
inline DB& RF(DB &);
inline DB RF(){DB x; return RF(x);}
inline char* RS(char *s);
inline char& RC(char &c);
inline char RC();
inline char& RC(char &c){scanf(" %c", &c); return c;}
inline char RC(){char c; return RC(c);}
//inline char& RC(char &c){c = getchar(); return c;}
//inline char RC(){return getchar();}
template<class T> inline T& RDD(T &);
inline LL RDD(){LL x; return RDD(x);}
template<class T0, class T1> inline T0& RD(T0 &x0, T1 &x1){RD(x0), RD(x1); return x0;}
template<class T0, class T1, class T2> inline T0& RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2); return x0;}
template<class T0, class T1, class T2, class T3> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3); return x0;}
template<class T0, class T1, class T2, class T3, class T4> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6); return x0;}
template<class T0, class T1> inline void OT(const T0 &x0, const T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5, const T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}
inline char& RC(char &a, char &b){RC(a), RC(b); return a;}
inline char& RC(char &a, char &b, char &c){RC(a), RC(b), RC(c); return a;}
inline char& RC(char &a, char &b, char &c, char &d){RC(a), RC(b), RC(c), RC(d); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e){RC(a), RC(b), RC(c), RC(d), RC(e); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g); return a;}
inline DB& RF(DB &a, DB &b){RF(a), RF(b); return a;}
inline DB& RF(DB &a, DB &b, DB &c){RF(a), RF(b), RF(c); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d){RF(a), RF(b), RF(c), RF(d); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e){RF(a), RF(b), RF(c), RF(d), RF(e); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f, DB &g){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g); return a;}
inline void RS(char *s1, char *s2){RS(s1), RS(s2);}
inline void RS(char *s1, char *s2, char *s3){RS(s1), RS(s2), RS(s3);}
template<class T0,class T1>inline void RDD(T0&a, T1&b){RDD(a),RDD(b);}
template<class T0,class T1,class T2>inline void RDD(T0&a, T1&b, T2&c){RDD(a),RDD(b),RDD(c);}
template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T> inline void CLR(T &A){A.clear();}
template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x), FLC(A6, x);}
template<class T> inline void CLR(priority_queue<T, vector<T>, less<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(priority_queue<T, vector<T>, greater<T> > &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(stack<T> &S){while (!S.empty()) S.pop();}
template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}
template<class T> inline bool EPT(T &a){return a.empty();}
template<class T> inline T& SRT(T &A){sort(ALL(A)); return A;}
template<class T, class C> inline T& SRT(T &A, C B){sort(ALL(A), B); return A;}
template<class T> inline T& RVS(T &A){reverse(ALL(A)); return A;}
template<class T> inline T& UNQQ(T &A){A.resize(unique(ALL(A))-A.begin());return A;}
template<class T> inline T& UNQ(T &A){SRT(A);return UNQQ(A);}
//}
/** Constant List .. **/ //{
const int MOD = int(1e9) + 7;
const int INF = 0x3f3f3f3f;
const LL INFF = 0x3f3f3f3f3f3f3f3fLL;
const DB EPS = 1e-9;
const DB OO = 1e20;
const DB PI = acos(-1.0); //M_PI;
const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};
//}
/** Add On .. **/ //{
// <<= '0. Nichi Joo ., //{
template<class T> inline T& checkMin(T &a,const T b){if (b<a) a=b;return a;}
template<class T> inline T& checkMax(T &a,const T b){if (a<b) a=b;return a;}
template<class T> inline T& checkMin(T &a, T &b, const T x){checkMin(a, x), checkMin(b, x);return a;}
template<class T> inline T& checkMax(T &a, T &b, const T x){checkMax(a, x), checkMax(b, x);return a;}
template <class T, class C> inline T& checkMin(T& a, const T b, C c){if (c(b,a)) a = b;return a;}
template <class T, class C> inline T& checkMax(T& a, const T b, C c){if (c(a,b)) a = b;return a;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}
template<class T> inline T max(T a, T b, T c, T d){return max(max(a, b), max(c, d));}
template<class T> inline T min(T a, T b, T c, T d, T e){return min(min(min(a,b),min(c,d)),e);}
template<class T> inline T max(T a, T b, T c, T d, T e){return max(max(max(a,b),max(c,d)),e);}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
template<class T> inline T ceil(T x, T y){return (x - 1) / y + 1;}
template<class T> T abs(T x){return x>0?x:-x;}
inline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}
inline int sgn(DB x, DB y){return sgn(x - y);}
inline DB cos(DB a, DB b, DB c){return (sqr(a)+sqr(b)-sqr(c))/(2*a*b);}
inline DB cot(DB x){return 1./tan(x);};
inline DB sec(DB x){return 1./cos(x);};
inline DB csc(DB x){return 1./sin(x);};
//}
// <<= '1. Bitwise Operation ., //{
namespace BO{
inline bool _1(int x, int i){return bool(x&1<<i);}
inline bool _1(LL x, int i){return bool(x&1LL<<i);}
inline LL _1(int i){return 1LL<<i;}
inline LL _U(int i){return _1(i) - 1;};
inline int reverse_bits(int x){
x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);
x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);
x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);
x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);
x = ((x >>16) & 0x0000ffff) | ((x <<16) & 0xffff0000);
return x;
}
inline LL reverse_bits(LL x){
x = ((x >> 1) & 0x5555555555555555LL) | ((x << 1) & 0xaaaaaaaaaaaaaaaaLL);
x = ((x >> 2) & 0x3333333333333333LL) | ((x << 2) & 0xccccccccccccccccLL);
x = ((x >> 4) & 0x0f0f0f0f0f0f0f0fLL) | ((x << 4) & 0xf0f0f0f0f0f0f0f0LL);
x = ((x >> 8) & 0x00ff00ff00ff00ffLL) | ((x << 8) & 0xff00ff00ff00ff00LL);
x = ((x >>16) & 0x0000ffff0000ffffLL) | ((x <<16) & 0xffff0000ffff0000LL);
x = ((x >>32) & 0x00000000ffffffffLL) | ((x <<32) & 0xffffffff00000000LL);
return x;
}
template<class T> inline bool odd(T x){return x&1;}
template<class T> inline bool even(T x){return !odd(x);}
template<class T> inline T low_bit(T x) {return x & -x;}
template<class T> inline T high_bit(T x) {T p = low_bit(x);while (p != x) x -= p, p = low_bit(x);return p;}
template<class T> inline T cover_bit(T x){T p = 1; while (p < x) p <<= 1;return p;}
template<class T> inline int cover_idx(T x){int p = 0; while (_1(p) < x ) ++p; return p;}
inline int clz(int x){return __builtin_clz(x);}
inline int clz(LL x){return __builtin_clzll(x);}
inline int ctz(int x){return __builtin_ctz(x);}
inline int ctz(LL x){return __builtin_ctzll(x);}
inline int lg2(int x){return !x ? -1 : 31 - clz(x);}
inline int lg2(LL x){return !x ? -1 : 63 - clz(x);}
inline int low_idx(int x){return !x ? -1 : ctz(x);}
inline int low_idx(LL x){return !x ? -1 : ctz(x);}
inline int high_idx(int x){return lg2(x);}
inline int high_idx(LL x){return lg2(x);}
inline int parity(int x){return __builtin_parity(x);}
inline int parity(LL x){return __builtin_parityll(x);}
inline int count_bits(int x){return __builtin_popcount(x);}
inline int count_bits(LL x){return __builtin_popcountll(x);}
} using namespace BO;//}
// <<= '2. Number Theory .,//{
namespace NT{
#define gcd __gcd
inline LL lcm(LL a, LL b){return a*b/gcd(a,b);}
inline void INC(int &a, int b){a += b; if (a >= MOD) a -= MOD;}
inline int sum(int a, int b){a += b; if (a >= MOD) a -= MOD; return a;}
/* 模数两倍刚好超 int 时。
inline int sum(uint a, int b){a += b; a %= MOD;if (a < 0) a += MOD; return a;}
inline void INC(int &a, int b){a = sum(a, b);}
*/
inline void DEC(int &a, int b){a -= b; if (a < 0) a += MOD;}
inline int dff(int a, int b){a -= b; if (a < 0) a += MOD; return a;}
inline void MUL(int &a, int b){a = (LL)a * b % MOD;}
inline int pdt(int a, int b){return (LL)a * b % MOD;}
inline int gcd(int m, int n, int &x, int &y){
x = 1, y = 0; int xx = 0, yy = 1, q;
while (1){
q = m / n, m %= n;
if (!m){x = xx, y = yy; return n;}
DEC(x, pdt(q, xx)), DEC(y, pdt(q, yy));
q = n / m, n %= m;
if (!n) return m;
DEC(xx, pdt(q, x)), DEC(yy, pdt(q, y));
}
}
inline int sum(int a, int b, int c){return sum(a, sum(b, c));}
inline int sum(int a, int b, int c, int d){return sum(sum(a, b), sum(c, d));}
inline int pdt(int a, int b, int c){return pdt(a, pdt(b, c));}
inline int pdt(int a, int b, int c, int d){return pdt(pdt(a, b), pdt(c, d));}
inline int pow(int a, LL b){
int c(1); while (b){
if (b&1) MUL(c, a);
MUL(a, a), b >>= 1;
}
return c;
}
template<class T> inline T pow(T a, LL b){
T c(1); while (b){
if (b&1) c *= a;
a *= a, b >>= 1;
}
return c;
}
template<class T> inline T pow(T a, int b){
return pow(a, (LL)b);
}
inline int _I(int b){
int a = MOD, x1 = 0, x2 = 1, q; while (1){
q = a / b, a %= b;
if (!a) return x2;
DEC(x1, pdt(q, x2));
q = b / a, b %= a;
if (!b) return x1;
DEC(x2, pdt(q, x1));
}
}
inline void DIV(int &a, int b){MUL(a, _I(b));}
inline int qtt(int a, int b){return pdt(a, _I(b));}
struct Int{
int val;
operator int() const{return val;}
Int(int val = 0):val(val){
val %= MOD; if (val < 0) val += MOD;
}
Int(LL _val){
_val %= MOD; if (_val < 0) _val += MOD;
val = _val;
}
Int& operator +=(const int& rhs){INC(val, rhs);rTs;}
Int operator +(const int& rhs) const{return sum(val, rhs);}
Int& operator -=(const int& rhs){DEC(val, rhs);rTs;}
Int operator -(const int& rhs) const{return dff(val, rhs);}
Int& operator *=(const int& rhs){MUL(val, rhs);rTs;}
Int operator *(const int& rhs) const{return pdt(val, rhs);}
Int& operator /=(const int& rhs){DIV(val, rhs);rTs;}
Int operator /(const int& rhs) const{return qtt(val, rhs);}
Int operator-()const{return MOD-*this;}
};
} using namespace NT;//}
//}
/** I/O Accelerator Interface .. **/ //{
#define g (c=getchar())
#define d isdigit(g)
#define p x=x*10+c-'0'
#define n x=x*10+'0'-c
#define pp l/=10,p
#define nn l/=10,n
template<class T> inline T& RD(T &x){
char c;while(!d);x=c-'0';while(d)p;
return x;
}
template<class T> inline T& RDD(T &x){
char c;while(g,c!='-'&&!isdigit(c));
if (c=='-'){x='0'-g;while(d)n;}
else{x=c-'0';while(d)p;}
return x;
}
inline DB& RF(DB &x){
//scanf("%lf", &x);
char c;while(g,c!='-'&&c!='.'&&!isdigit(c));
if(c=='-')if(g=='.'){x=0;DB l=1;while(d)nn;x*=l;}
else{x='0'-c;while(d)n;if(c=='.'){DB l=1;while(d)nn;x*=l;}}
else if(c=='.'){x=0;DB l=1;while(d)pp;x*=l;}
else{x=c-'0';while(d)p;if(c=='.'){DB l=1;while(d)pp;x*=l;}}
return x;
}
#undef nn
#undef pp
#undef n
#undef p
#undef d
#undef g
inline char* RS(char *s){
//gets(s);
scanf("%s", s);
return s;
}
LL last_ans; int Case; template<class T> inline void OT(const T &x){
//printf("Case #%d: ", ++Case);
//printf("%lld\n", x);
//printf("%.9f\n", x);
printf("%d\n", x);
//cout << x << endl;
//last_ans = x;
}
//}
//}/* .................................................................................................................................. */
const int N = 2009;
int cards[N], bonus[N], n;
int A, B;
int f0(){
if (A > 2*B) return 4;
if (A == 2*B) return 2;
if (A >= B) return 0;
return -4;
}
vector<pair<int, pair<int, int> > > I;
void Add(int a, int j, int b){
if (a < 0 || a > A) return;
I.PB(MP(a, MP(j, b)));
}
//a = A - B
/*
19
10
11
10
0
2 A+a = 2B
3 A+a > 2B
0 A-a < B
A-B < 2B-A
2A < 3B
*/
int f(int i){
I.clear(), A = cards[i];
int z = 0; REP(j, n) if (i != j){
B = cards[j], z += f0(), bonus[j] = f0();
// cout << A << " " << B << endl;
if (A > 2*B){
Add(A-2*B, j, 3);
Add(A-2*B+1, j, 2);
}
else if (A == 2*B){
Add(A-B, j, 0);
}
else if (A > B){
VII II;
II.PB(MP(2*B-A, 1)), II.PB(MP(2*B-A+1, 3));
II.PB(MP(A-B+1, 0));
SRT(II); int b = INF;
for (int ii=0;ii<SZ(II);){
int a = II[ii].fi, bb = b == INF ? 0 : bb;
do{
checkMin(b, II[ii++].se);
} while (ii<SZ(II) && II[ii].fi == II[ii-1].fi);
if (b != bb) Add(a, j, b);
//cout << " " << a << " " << b << endl;
}
}
else if (A < B){
Add(B-A, j, -2);
}
}
int zz = z; SRT(I);
//cout << "A:" << A << endl;
//cout << " " << 0 << " " << zz << endl;
for (int i=0;i<SZ(I);){
do{
int id = I[i].se.fi, bo = I[i].se.se, d = bo - bonus[id];
zz += d, bonus[id] = bo, ++i;
}while (i<SZ(I) && I[i-1].fi == I[i].fi);
// cout << " " << I[i-1].fi << " " << zz << endl;
checkMax(z, zz);
}
//cout << z << endl;
return z;
}
class AliceAndFriends {
public:
double getMoney(vector <int> cards) {
n = cards.size(); REP(i, n) ::cards[i] = cards[i];
int res = 0; REP(i, n) res += f(i);
return (DB)res/n/4;
}
};
//10 9
//10 9
//0, A+a=2B, 1, A+a>2B, 2
// 2B-A 2B-a+1
// 8 9
// A-a<B, 0
// A-B+1
// 2
//0,
//9 10
//-4, A+a=B, -3, A+a>B, -2
// BEGIN CUT HERE
namespace moj_harness {
int run_test_case(int);
void run_test(int casenum = -1, bool quiet = false) {
if (casenum != -1) {
if (run_test_case(casenum) == -1 && !quiet) {
cerr << "Illegal input! Test case " << casenum << " does not exist." << endl;
}
return;
}
int correct = 0, total = 0;
for (int i=0;; ++i) {
int x = run_test_case(i);
if (x == -1) {
if (i >= 100) break;
continue;
}
correct += x;
++total;
}
if (total == 0) {
cerr << "No test cases run." << endl;
} else if (correct < total) {
cerr << "Some cases FAILED (passed " << correct << " of " << total << ")." << endl;
} else {
cerr << "All " << total << " tests passed!" << endl;
}
}
static const double MAX_DOUBLE_ERROR = 1e-9; static bool topcoder_fequ(double expected, double result) { if (isnan(expected)) { return isnan(result); } else if (isinf(expected)) { if (expected > 0) { return result > 0 && isinf(result); } else { return result < 0 && isinf(result); } } else if (isnan(result) || isinf(result)) { return false; } else if (fabs(result - expected) < MAX_DOUBLE_ERROR) { return true; } else { double mmin = min(expected * (1.0 - MAX_DOUBLE_ERROR), expected * (1.0 + MAX_DOUBLE_ERROR)); double mmax = max(expected * (1.0 - MAX_DOUBLE_ERROR), expected * (1.0 + MAX_DOUBLE_ERROR)); return result > mmin && result < mmax; } }
double moj_relative_error(double expected, double result) { if (isnan(expected) || isinf(expected) || isnan(result) || isinf(result) || expected == 0) return 0; return fabs(result-expected) / fabs(expected); }
int verify_case(int casenum, const double &expected, const double &received, clock_t elapsed) {
cerr << "Example " << casenum << "... ";
string verdict;
vector<string> info;
char buf[100];
if (elapsed > CLOCKS_PER_SEC / 200) {
sprintf(buf, "time %.2fs", elapsed * (1.0/CLOCKS_PER_SEC));
info.push_back(buf);
}
if (topcoder_fequ(expected, received)) {
verdict = "PASSED";
double rerr = moj_relative_error(expected, received);
if (rerr > 0) {
sprintf(buf, "relative error %.3e", rerr);
info.push_back(buf);
}
} else {
verdict = "FAILED";
}
cerr << verdict;
if (!info.empty()) {
cerr << " (";
for (int i=0; i<(int)info.size(); ++i) {
if (i > 0) cerr << ", ";
cerr << info[i];
}
cerr << ")";
}
cerr << endl;
if (verdict == "FAILED") {
cerr << " Expected: " << expected << endl;
cerr << " Received: " << received << endl;
}
return verdict == "PASSED";
}
int run_test_case(int casenum) {
switch (casenum) {
case 0: {
int cards[] = {10, 1};
double expected__ = 0.0;
clock_t start__ = clock();
double received__ = AliceAndFriends().getMoney(vector <int>(cards, cards + (sizeof cards / sizeof cards[0])));
return verify_case(casenum, expected__, received__, clock()-start__);
}
case 1: {
int cards[] = {10, 9};
double expected__ = -0.25;
clock_t start__ = clock();
double received__ = AliceAndFriends().getMoney(vector <int>(cards, cards + (sizeof cards / sizeof cards[0])));
return verify_case(casenum, expected__, received__, clock()-start__);
}
case 2: {
int cards[] = {1, 3};
double expected__ = 0.0;
clock_t start__ = clock();
double received__ = AliceAndFriends().getMoney(vector <int>(cards, cards + (sizeof cards / sizeof cards[0])));
return verify_case(casenum, expected__, received__, clock()-start__);
}
case 3: {
int cards[] = {1000000000, 1000000000};
double expected__ = 0.0;
clock_t start__ = clock();
double received__ = AliceAndFriends().getMoney(vector <int>(cards, cards + (sizeof cards / sizeof cards[0])));
return verify_case(casenum, expected__, received__, clock()-start__);
}
case 4: {
int cards[] = {42, 468, 335, 501, 170, 725, 479, 359, 963, 465, 706, 146, 282, 828, 962, 492, 996, 943, 828, 437, 392, 605, 903, 154, 293, 383, 422, 717, 719, 896, 448, 727, 772, 539, 870, 913, 668, 300, 36, 895, 704, 812, 323, 334, 674, 665, 142, 712, 254, 869};
double expected__ = -9.095;
clock_t start__ = clock();
double received__ = AliceAndFriends().getMoney(vector <int>(cards, cards + (sizeof cards / sizeof cards[0])));
return verify_case(casenum, expected__, received__, clock()-start__);
}
// custom cases
/*
case 5: {
int cards[] = ;
double expected__ = ;
clock_t start__ = clock();
double received__ = AliceAndFriends().getMoney(vector <int>(cards, cards + (sizeof cards / sizeof cards[0])));
return verify_case(casenum, expected__, received__, clock()-start__);
}
case 6: {
int cards[] = ;
double expected__ = ;
clock_t start__ = clock();
double received__ = AliceAndFriends().getMoney(vector <int>(cards, cards + (sizeof cards / sizeof cards[0])));
return verify_case(casenum, expected__, received__, clock()-start__);
}*/
/* case 7: {
int cards[] = ;
double expected__ = ;
clock_t start__ = clock();
double received__ = AliceAndFriends().getMoney(vector <int>(cards, cards + (sizeof cards / sizeof cards[0])));
return verify_case(casenum, expected__, received__, clock()-start__);
}*/
default:
return -1;
}
}
}
int main(int argc, char *argv[]) {
if (argc == 1) {
moj_harness::run_test();
} else {
for (int i=1; i<argc; ++i)
moj_harness::run_test(atoi(argv[i]));
}
}
// END CUT HERE
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