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x:<:+/(*((*/@:<:@~.@q:)%(*/@~.@q:)))"0>:i.1e6

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(print([rec(f a b)([^c(if(>(imag-part c)12e3)0(+(f a c)(f c b)1))](+ a b))]1+2i 1+3i))

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nchains =: 3 (169 363601 1454) } 2 (871 872 45361 45362) } 0 $~ 1 + 6 * !9

solve =: 3 : 0
  if. 0 = n =. y { nchains do.
     z =. (+/@:!@(10&#.inv)) y
     nchains =: (n =. (>:@solve@(z&[)) ` 1: @. (=&z) y) y } nchains
  end.
n
)
+/ 60 = solve"0 >:i.1e6

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v =: 0 $~ >:15e5
draw =: 3 : 0
  i =. L =. +:m*m+n [ (n =. a+x) [ (m =. b+y) [ ('a b x y' =. y)
  if. 2 | m-n do.
    for_i. L*>:i.<.L%~<:#v do. v =: (>:i{v)i}v end.
  end.
  if. L < #v do. draw a;b;n;m [ (draw n;m;x;y) end.
)
((1!:2)&2) +/ 1 = v [ (draw 0 1 1 1)

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q =: p M.
p =: 4 : '(((>:x)&q)+((x&q)@(-&x))) ` (0: ` 1: @. (x&=)) @. (x&>:) y'
((1!:2)&2) <: 1 q 100

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g =: p:&(] ` 0: @. (<&0))
q =: p M.
p =: 4 : '(((x-g y)&q) + (x&q@<:)) ` (0: ` 1: @. (x=0&[)) @. ((x<2)&+.@(<&0)) y'
f =: 3 : '(y q (p:^:_1)y) + (0: ` _1: @. (y&=) p:(p:^:_1)y)'
((1!:2)&2) >:{:([^:((5000&<)@f@])>:)^:a: 3

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q =: p M.
p =: 4 : '(((x-p:(0>.y))&q) + (x&q@<:)) ` (0: ` 1: @. (x=0&[)) @. ((x<2)&+.@(<&0)) y'
f =: 3 : '(y q (p:^:_1)y) + (0: ` _1: @. (y&=) p:(p:^:_1)y)'
((1!:2)&2) >:{:([^:((5000&<)@f@])>:)^:a: 3

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// g++ -O3 78.cpp; time ./a => 0.08s

#include <vector>
#include <iostream>

enum { m = (int)1e6, virgin = m };
std::vector<int> pns(100, virgin);

int p(int n)
{

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#!r6rs

(import (rnrs) (only (srfi :1) iota))

(define (sqrt=irrational? x)
  (not (= x (expt (floor (sqrt x)) 2))))
(define (exact-sqrt x)
  (let-values ([(a b) (exact-integer-sqrt x)]) a))
(define (sum-digits x)
  (if (< x 10) x (+ (mod x 10) (sum-digits (div x 10)))))

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(*:@(+/@:>:@:i.) - +/@:*:@:>:@:i.) 100