import std.algorithm, std.container, std.conv, std.math, std.range, std.typecons, std.stdio, std.string; auto rdsp(){return readln.splitter;} void pick(R,T)(ref R r,ref T t){t=r.front.to!T;r.popFront;} void readV(T...)(ref T t){auto r=rdsp;foreach(ref v;t)pick(r,v);} void main() { int n; readV(n); auto p = primes(n*3).assumeSorted; auto ca = new int[](n*2), cb = new int[](n*2), ans = 0L; foreach (b; p.upperBound(2).lowerBound(n+1)) { ca[] = 0; foreach (c; p.upperBound(b).lowerBound(n+1)) ++ca[b+c]; foreach (i; 1..n+1) ans += ca[i*2]*cb[i*2]; foreach (d; p.upperBound(b).lowerBound(b+n*2+1)) ++cb[d-b]; } writeln(ans); } pure T[] primes(T)(T n) { import std.algorithm, std.bitmanip, std.conv, std.range; auto sieve = BitArray(); sieve.length((n+1)/2); sieve = ~sieve; foreach (p; 1..((nsqrt(n)-1)/2+1)) if (sieve[p]) for (auto q = p*3+1; q < (n+1)/2; q += p*2+1) sieve[q] = false; auto r = sieve.bitsSet.map!(to!T).map!("a*2+1").array; r[0] = 2; return r; } pure T factor(T)(T n, const T[] p) { auto ma = nsqrt(n)+1; foreach (pi; p) if (pi > ma) return n; else if (n%pi == 0) return pi; return n; } pure T nsqrt(T)(T n) { import std.algorithm, std.conv, std.range, core.bitop; if (n <= 1) return n; T m = T(1) << (n.bsr/2+1); return iota(1, m).map!"a*a".assumeSorted!"a <= b".lowerBound(n).length.to!T; }