Problem:
ゴールドバッハの予想
4 以上の偶数は 2 つの素数の和で表すことができるということが知られています。これはゴールドバッハ予想といい、コンピュータの計算によりかなり大きな数まで正しいことが確かめられています。例えば、10 は、7 + 3、5 + 5 の 2 通りの素数の和で表すことができます。
整数
n
を入力し、
n
を 2 つの素数の和で表す組み合わせ数が何通りあるかを出力するプログラムを作成してください。ただし、
n
は 4 以上、50,000 以下とします。また、入力される
n
は偶数であるとはかぎりません。
Input
複数のデータセットが与えられます。各データセットに
n
が１行に与えられます。
n
が 0 のとき入力の最後とします。データセットの数は 10,000 を超えません。
Output
各データセットに対して、
n
を 2 つの素数の和で表す組み合わせ数を１行に出力して下さい。
Sample Input
10
11
0
Output for the Sample Input
2
0

Submitted solutions:

code_snippet: #include<bits/stdc++.h>
using namespace std;

int main(void){
  vector<int> yakusu(50001, -1);
  for(int i=2; i<=50000; i++){
    if(yakusu[i]!=-1) continue;
    int copy=i;
    while(copy<=50000){
      if(yakusu[copy]==-1) yakusu[copy]=i;
      copy+=i;
    }
  }
  vector<int> prime;
  for(int i=2; i<=50000; i++){
    if(yakusu[i]==i) prime.push_back(i);
  }
  int m=prime.size();
  map<int, int> ans;
  for(int i=0; i<m-1; i++){
    for(int j=i; j<m; j++){
      ans[prime[i]+prime[j]]++;
    }
  }

  int n;
  while(cin >> n){
    if(n==0) break;
    cout << ans[n] << endl;
  }

  return 0;
}
accuracy: 1
time_ms: 710
memory_kb: 6100
final_rank: 20

code_snippet: #pragma region Macros

#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,fma,abm,mmx,avx,avx2")

#include <bits/extc++.h>
// #include <atcoder/all>
// using namespace atcoder;
using namespace std;
using namespace __gnu_pbds;

// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// using Bint = mp::cpp_int;
// using Bdouble = mp::number<mp::cpp_dec_float<256>>;
// Bdouble Beps = 0.00000000000000000000000000000001; // 1e-32
// const bool equals(Bdouble a, Bdouble b) { return mp::fabs(a - b) < Beps; }

#define pb emplace_back
#define int ll
#define endl '\n'
// #define unordered_map<int, int> gp_hash_table<int, int, custom_hash> 

#define sqrt __builtin_sqrtl
#define cbrt __builtin_cbrtl
#define hypot __builtin_hypotl

#define next asdnext
#define prev asdprev

using ll = long long;
using ld = long double;
const ld PI = acosl(-1);
const int INF = 1 << 30;
const ll INFL = 1LL << 61;
// const int MOD = 998244353;
const int MOD = 1000000007;

const ld EPS = 1e-10;
const bool equals(ld a, ld b) { return fabs((a) - (b)) < EPS; }

const vector<int> dx = {0, 1, 0, -1, 1, 1, -1, -1}; // → ↓ ← ↑ ↘ ↙ ↖ ↗
const vector<int> dy = {1, 0, -1, 0, 1, -1, -1, 1};

struct Edge {
    int from, to, cost;
    Edge() : from(-1), to(-1), cost(-1) {}
    Edge(int to, int cost) : to(to), cost(cost) {}
    Edge(int from, int to, int cost) : from(from), to(to), cost(cost) {}
    bool operator ==(const Edge& e) {
        return this->from == e.from && this->to == e.to && this->cost == e.cost;
    }
    bool operator !=(const Edge& e) {
        return this->from != e.from or this->to != e.to or this->cost != e.cost;
    }
};

chrono::system_clock::time_point start;
__attribute__((constructor))
void constructor() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(10);
    start = chrono::system_clock::now();
}

random_device seed_gen;
mt19937_64 rng(seed_gen());
uniform_int_distribution<int> dist_x(0, 1e9);
struct RNG {
    unsigned Int(unsigned l, unsigned r) {
        return dist_x(rng) % (r - l + 1) + l;
    }
    ld Double() {
        return ld(dist_x(rng)) / 1e9;
    }
} rnd;

using i64 = ll;
// using i64 = uint64_t;
// bit演算, x==0の場合は例外処理した方がよさそう. 区間は [l, r)
i64 lrmask(i64 l, i64 r) { return (1LL << r) - (1LL << l); }
i64 sub_bit(i64 x, i64 l, i64 r) { i64 b = x & ((1LL << r) - (1LL << l)); return b >> l; } // r溢れ可
i64 bit_width(i64 x) { return 64 - __builtin_clzll(x) + (x == 0); }

i64 popcount(i64 x) { return __builtin_popcountll(x); }
i64 popcount(i64 x, i64 l, i64 r) { return __builtin_popcountll(sub_bit(x, l, r)); }
i64 unpopcount(i64 x) { return bit_width(x) - __builtin_popcountll(x); }
i64 unpopcount(i64 x, i64 l, i64 r) { return r - l - __builtin_popcountll(sub_bit(x, l, r)); }
bool is_pow2(i64 x) { return __builtin_popcountll(x) == 1; }

i64 top_bit(i64 x) { return 63 - __builtin_clzll(x);} // 2^kの位 (x > 0)
i64 bot_bit(i64 x) { return __builtin_ctz(x);} // 2^kの位 (x > 0)
// i64 next_bit(i64 x, i64 k) { return 0; }
// i64 prev_bit(i64 x, i64 k) { return 0; }
// i64 kth_bit(i64 x, i64 k) { return 0; }
i64 MSB(i64 x) { if (x == 0) return 0; return 1LL << (63 - __builtin_clzll(x)); } // mask
i64 LSB(i64 x) { return (x & -x); } // mask

i64 countl_zero(i64 x) { return __builtin_clzll(x); }
i64 countl_one(i64 x) {
    i64 ret = 0, k = 63 - __builtin_clzll(x);
    while (k != -1 && (x & (1LL << k))) { k--; ret++; }
    return ret;
}
i64 countr_zero(i64 x) { return __builtin_ctzll(x); } // x==0のとき64が返ることに注意
i64 countr_one(i64 x) { i64 ret = 0; while (x & 1) { x >>= 1; ret++; } return ret; }

i64 floor_log2(i64 x) { if (x == 0) return 0; return 63 - __builtin_clzll(x); }
i64 bit_floor(i64 x) { if (x == 0) return 0; return 1LL << (63 - __builtin_clzll(x)); } // MSBと同じ
i64 ceil_log2(i64 x) { if (x == 0) return 0; return 64 - __builtin_clzll(x - 1); }
i64 bit_ceil(i64 x) { if (x == 0) return 0; return 1LL << (64 - __builtin_clzll(x - 1)); }

i64 rotl(i64 x, i64 k) { // 有効bit内でrotate. オーバーフロー注意
    i64 w = bit_width(x); k %= w;
    return ((x << k) | (x >> (w - k))) & ((1LL << w) - 1);
}
// i64 rotl(i64 x, i64 l, i64 m, i64 r) {}
i64 rotr(i64 x, i64 k) {
    i64 w = bit_width(x); k %= w;
    return ((x >> k) | (x << (w - k))) & ((1LL << w) - 1);
}
// i64 rotr(i64 x, i64 l, i64 m, i64 r) {}
i64 bit_reverse(i64 x) { // 有効bit内で左右反転
    i64 r = 0, w = bit_width(x);
    for (i64 i = 0; i < w; i++) r |= ((x >> i) & 1) << (w - i - 1);
    return r;
}
// i64 bit_reverse(i64 x, i64 l, i64 r) { return 0; }

bool is_palindrome(i64 x) { return x == bit_reverse(x); }
bool is_palindrome(i64 x, i64 l, i64 r) { i64 b = sub_bit(x, l, r); return b == bit_reverse(b); }
i64 concat(i64 a, i64 b) { return (a << bit_width(b)) | b; } // オーバーフロー注意
i64 erase(i64 x, i64 l, i64 r) { return x>>r<<l | x&(1LL<<l - 1); } // [l, r) をカット

i64 hamming(i64 a, i64 b) { return __builtin_popcountll(a ^ b); }
i64 hamming(i64 a, i64 b, i64 l, i64 r) { return __builtin_popcountll(sub_bit(a, l, r) ^ sub_bit(b, l, r)); }
i64 compcount(i64 x) { return (__builtin_popcountll(x ^ (x >> 1)) + (x & 1)) / 2; }
i64 compcount2(i64 x) { return compcount(x & (x >> 1)); } // 長さ2以上の連結成分の個数
i64 adjacount(i64 x) { return __builtin_popcountll(x & (x >> 1)); } // 隣接する1のペアの個数

i64 next_combination(i64 x) {
    i64 t = x | (x - 1); return (t + 1) | (((~t & -~t) - 1) >> (__builtin_ctz(x) + 1));
}


__int128_t POW(__int128_t x, int n) {
    __int128_t ret = 1;
    assert(n >= 0);
    if (x == 1 or n == 0) ret = 1;
    else if (x == -1 && n % 2 == 0) ret = 1; 
    else if (x == -1) ret = -1; 
    else if (n % 2 == 0) {
        assert(x < INFL);
        ret = POW(x * x, n / 2);
    } else {
        assert(x < INFL);
        ret = x * POW(x, n - 1);
    }
    return ret;
}
int per(int x, int y) { // x = qy + r (0 <= r < y) を満たすq
    assert(y != 0);
    if (x >= 0 && y > 0) return x / y;
    if (x >= 0 && y < 0) return x / y - (x % y < 0);
    if (x < 0 && y < 0) return x / y + (x % y < 0);
    return x / y - (x % y < 0); //  (x < 0 && y > 0) 
}
int mod(int x, int y) { // x = qy + r (0 <= r < y) を満たすr
    assert(y != 0);
    if (x >= 0) return x % y;
    __int128_t ret = x % y; // (x < 0)
    ret += (__int128_t)abs(y) * INFL;
    ret %= abs(y);
    return ret;
}
int floor(int x, int y) { // (ld)x / y 以下の最大の整数
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return x >= 0 ? x / y : (x + 1) / y - 1;
}
int ceil(int x, int y) { // (ld)x / y 以上の最小の整数
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return x > 0 ? (x - 1) / y + 1 : x / y;
}
int round(int x, int y) {
    assert(y != 0);
    return (x * 2 + y) / (y * 2);
}
int round(int x, int y, int k) { // (ld)(x/y)を10^kの位に関して四捨五入
    assert(y != 0); // TODO
    return INF;
}
int round2(int x, int y) { // 五捨五超入 // 未verify
    assert(y != 0);
    if (y < 0) y = -y, x = -x;
    int z = z / y;
    if ((z * 2 + 1) * y <= y * 2) z++;
    return z;
}
// int round(ld x, int k) { // xを10^kの位に関して四捨五入
// }
// int floor(ld x, int k) { // xを10^kの位に関してflooring
// }
// int ceil(ld x, int k) { // xを10^kの位に関してceiling
// }
// int kth(int x, int y, int k) { // x / yの10^kの位の桁
// }
int floor(ld x, ld y) { // 誤差対策TODO
    assert(!equals(y, 0));
    return floor(x / y);
    // floor(x) = ceil(x - 1) という話も
}
int ceil(ld x, ld y) { // 誤差対策TODO // ceil(p/q) = -floor(-(p/q))らしい
    assert(!equals(y, 0));
    return ceil(x / y);
    // ceil(x) = floor(x + 1)
}
int perl(ld x, ld y) { // x = qy + r (0 <= r < y, qは整数) を満たす q
    // 未verify. 誤差対策TODO. EPS外してもいいかも。
    assert(!equals(y, 0));
    if (x >= 0 && y > 0) return floor(x / y)+EPS;
    if (x >= 0 && y < 0) return -floor(x / fabs(y));
    if (x < 0 && y < 0) return floor(x / y) + (x - floor(x/y)*y < -EPS);
    return floor(x / y) - (x - floor(x/y)*y < -EPS); //  (x < 0 && y > 0) 
}
ld modl(ld x, ld y) { // x = qy + r (0 <= r < y, qは整数) を満たす r
    // 未verify. 誤差対策TODO. -0.0が返りうる。
    assert(!equals(y, 0));
    if (x >= 0) return x - fabs(y)*fabs(per(x, y));
    return x - fabs(y)*floor(x, fabs(y));
}
int seisuu(ld x) { return (int)x; } // 整数部分. 誤差対策TODO
// 正なら+EPS, 負なら-EPSしてから、文字列に直して小数点以下を捨てる?
int seisuu(int x, int y) {
    assert(y != 0);
    return x / y;
}
int seisuu(ld x, ld y) { // 誤差対策TODO
    assert(!equals(y, 0));
    return (int)(x / y);
}

template <class T> pair<T, T> max(const pair<T, T> &a, const pair<T, T> &b) {
    if (a.first > b.first or a.first == b.first && a.second > b.second) return a;
    return b;
}
template <class T> pair<T, T> min(const pair<T, T> &a, const pair<T, T> &b) {
    if (a.first < b.first or a.first == b.first && a.second < b.second) return a;
    return b;
}

template <class T> bool chmax(T &a, const T& b) {
    if (a < b) { a = b; return true; } return false;
}
template <class T> bool chmin(T &a, const T& b) {
    if (a > b) { a = b; return true; } return false;
}
template <class T> T mid(T a, T b, T c) { // 誤差対策TODO
    return a + b + c - max({a, b, c}) - min({a, b, c});
}
template <class T> void Sort(T &a, T &b, bool rev = false) { 
    if (rev == false) {  // TODO テンプレート引数
        if (a > b) swap(a, b);
    } else {
        if (b > a) swap(b, a);
    }
}
template <class T> void sort(T &a, T &b, T &c, bool rev = false) {
    if (rev == false) { 
        if (a > b) swap(a, b); if (a > c) swap(a, c); if (b > c) swap(b, c);
    } else {
        if (c > b) swap(c, b); if (c > a) swap(c, a); if (b > a) swap(b, a);
    }
}
template <class T> void sort(T &a, T &b, T &c, T &d, bool rev = false) {
    if (rev == false) { 
        if (a > b) swap(a, b); if (a > c) swap(a, c);  if (a > d) swap(a, d);
        if (b > c) swap(b, c); if (b > d) swap(b, d); if (c > d) swap(c, d);
    } else {
        if (d > c) swap(d, c); if (d > b) swap(d, b); if (d > a) swap(d, a);
        if (c > b) swap(c, b); if (c > a) swap(c, a); if (b > a) swap(b, a);
    }
}

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

class Compress {
public:
    int sz = 0;
    // gp_hash_table<int, int, custom_hash> Z, UZ;
    unordered_map<int, int> Z;    // 元の値 -> 圧縮した値
    unordered_map<int, int> UZ;   // 圧縮した値 -> 元の値

    Compress(const vector<int> &V, int base = 0) {
        this->sz = base;
        set<int> s(V.begin(), V.end());

        for (int x : s) {
            this->Z[x] = this->sz;
            this->UZ[this->sz] = x;
            this->sz++;
        }
    }
    
    Compress(const vector<int> &V1, const vector<int> &V2, int base = 0) {
        this->sz = base;
        vector<int> V3 = V2;
        V3.insert(V3.end(), V1.begin(), V1.end());
        set<int> s(V3.begin(), V3.end());

        for (int x : s) {
            this->Z[x] = this->sz;
            this->UZ[this->sz] = x;
            this->sz++;
        }
    }

    Compress(const vector<int> &V1, const vector<int> &V2, const vector<int> &V3, int base = 0) {
        this->sz = base;
        vector<int> V4 = V1;
        V4.insert(V4.end(), V2.begin(), V2.end());
        V4.insert(V4.end(), V3.begin(), V3.end());
        set<int> s(V4.begin(), V4.end());

        for (int x : s) {
            this->Z[x] = this->sz;
            this->UZ[this->sz] = x;
            this->sz++;
        }
    }

    Compress(const vector<int> &V1, const vector<int> &V2,
            const vector<int> &V3, const vector<int> &V4, int base = 0) {
        this->sz = base;
        vector<int> V5 = V1;
        V5.insert(V5.end(), V2.begin(), V2.end());
        V5.insert(V5.end(), V3.begin(), V3.end());
        V5.insert(V5.end(), V4.begin(), V4.end());
        set<int> s(V5.begin(), V5.end());

        for (int x : s) {
            this->Z[x] = this->sz;
            this->UZ[this->sz] = x;
            this->sz++;
        }
    }

    vector<int> zip(const vector<int> &V) {
        vector<int> ret = V;
        for (int i = 0; i < (int)V.size(); i++) {
            ret[i] = Z[ret[i]];
        }
        return ret;
    }

    vector<int> unzip(const vector<int> &V) {
        vector<int> ret = V;
        for (int i = 0; i < (int)V.size(); i++) {
            ret[i] = UZ[ret[i]];
        }
        return ret;
    }

    int size() { return sz; }

    int encode(int x) { return Z[x]; }
    int decode(int x) {
        if (UZ.find(x) == UZ.end()) return -1; // xが元の配列に存在しないとき
        return UZ[x];
    }
};

class UnionFind {
public:
	UnionFind() = default;
    UnionFind(int N) : par(N), sz(N, 1) {
        iota(par.begin(), par.end(), 0);
    }
	int root(int x) {
		if (par[x] == x) return x;
		return (par[x] = root(par[x]));
	}
	bool unite(int x, int y) {
		int rx = root(x);
		int ry = root(y);
        if (rx == ry) return false;
		if (sz[rx] < sz[ry]) swap(rx, ry);
		sz[rx] += sz[ry];
		par[ry] = rx;
        return true;
	}
	bool issame(int x, int y) { return (root(x) == root(y)); }
	int size(int x) { return sz[root(x)]; }
    vector<vector<int>> groups(int N) {
        vector<vector<int>> G(N);
        for (int x = 0; x < N; x++) {
            G[root(x)].push_back(x);
        }
		G.erase( remove_if(G.begin(), G.end(),
            [&](const vector<int>& V) { return V.empty(); }), G.end());
        return G;
    }
private:
	vector<int> par, sz;
};

template<typename T>
struct BIT {
    int N;             // 要素数
    vector<T> bit[2];  // データの格納先
    BIT(int N_, int x = 0) {
        N = N_ + 1;
        bit[0].assign(N, 0); bit[1].assign(N, 0);
        if (x != 0) {
            for (int i = 0; i < N; i++) add(i, x);
        }
    }
    BIT(const vector<int> &A) {
        N = A.size() + 1;
        bit[0].assign(N, 0); bit[1].assign(N, 0);
        for (int i = 0; i < (int)A.size(); i++) add(i, A[i]);
    }
    void add_sub(int p, int i, T x) {
        while (i < N) { bit[p][i] += x; i += (i & -i); }
    }
    void add(int l, int r, T x) {
        add_sub(0, l + 1, -x * l); add_sub(0, r + 1, x * r);
        add_sub(1, l + 1, x); add_sub(1, r + 1, -x);
    }
    void add(int i, T x) { add(i, i + 1, x); }
    T sum_sub(int p, int i) {
        T ret = 0;
        while (i > 0) { ret += bit[p][i]; i -= (i & -i); }
        return ret;
    }
    T sum(int i) { return sum_sub(0, i) + sum_sub(1, i) * i; }
    T sum(int l, int r) { return sum(r) - sum(l); }
    T get(int i) { return sum(i, i + 1); }
    void set(int i, T x) { T s = get(i); add(i, -s + x); }
};

template<int mod> class Modint {
public:
    int val = 0;
    Modint(int x = 0) { while (x < 0) x += mod; val = x % mod; }
    Modint(const Modint &r) { val = r.val; }

    Modint operator -() { return Modint(-val); } // 単項
    Modint operator +(const Modint &r) { return Modint(*this) += r; }
    Modint operator +(const int &q) { Modint r(q); return Modint(*this) += r; }
    Modint operator -(const Modint &r) { return Modint(*this) -= r; }
    Modint operator -(const int &q) { Modint r(q); return Modint(*this) -= r; }
    Modint operator *(const Modint &r) { return Modint(*this) *= r; }
    Modint operator *(const int &q) { Modint r(q); return Modint(*this) *= r; }
    Modint operator /(const Modint &r) { return Modint(*this) /= r; }
    Modint operator /(const int &q) { Modint r(q); return Modint(*this) /= r; }
    
    Modint& operator ++() { val++; if (val >= mod) val -= mod; return *this; } // 前置
    Modint operator ++(signed) { ++*this; return *this; } // 後置
    Modint& operator --() { val--; if (val < 0) val += mod; return *this; }
    Modint operator --(signed) { --*this; return *this; }
    Modint &operator +=(const Modint &r) { val += r.val; if (val >= mod) val -= mod; return *this; }
    Modint &operator +=(const int &q) { Modint r(q); val += r.val; if (val >= mod) val -= mod; return *this; }
    Modint &operator -=(const Modint &r) { if (val < r.val) val += mod; val -= r.val; return *this; }
    Modint &operator -=(const int &q) { Modint r(q);  if (val < r.val) val += mod; val -= r.val; return *this; }
    Modint &operator *=(const Modint &r) { val = val * r.val % mod; return *this; }
    Modint &operator *=(const int &q) { Modint r(q); val = val * r.val % mod; return *this; }
    Modint &operator /=(const Modint &r) {
        int a = r.val, b = mod, u = 1, v = 0;
        while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);}
        val = val * u % mod; if (val < 0) val += mod;
        return *this;
    }
    Modint &operator /=(const int &q) {
        Modint r(q); int a = r.val, b = mod, u = 1, v = 0;
        while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);}
        val = val * u % mod; if (val < 0) val += mod;
        return *this;
    }
    bool operator ==(const Modint& r) { return this -> val == r.val; }
    bool operator <(const Modint& r) { return this -> val < r.val; }
    bool operator >(const Modint& r) { return this -> val > r.val; }
    bool operator !=(const Modint& r) { return this -> val != r.val; }
};

using mint = Modint<MOD>;

istream &operator >>(istream &is, mint& x) {
    int t; is >> t; x = t; return (is);
}
ostream &operator <<(ostream &os, const mint& x) {
    return os << x.val;
}
mint modpow(const mint &x, int n) {
    if (n < 0) return (mint)1 / modpow(x, -n); // 未verify
    assert(n >= 0);
    if (n == 0) return 1;
    mint t = modpow(x, n / 2);
    t = t * t;
    if (n & 1) t = t * x;
    return t;
}

int modpow(__int128_t x, int n, int mod) {
    assert(n >= 0 && mod > 0); // TODO: n <= -1
    __int128_t ret = 1;
    while (n > 0) {
        if (n % 2 == 1) ret = ret * x % mod;
        x = x * x % mod;
        n /= 2;
    }
    return ret;
}
int modinv(__int128_t x, int mod) {
    assert(mod > 0);
    // assert(x > 0);
    if (x == 1 or x == 0) return 1;
    return mod - modinv(mod % x, mod) * (mod / x) % mod;
}

istream &operator >>(istream &is, __int128_t& x) {
    string S; is >> S;
    __int128_t ret = 0;
    int f = 1;
    if (S[0] == '-') f = -1; 
    for (int i = 0; i < S.length(); i++)
        if ('0' <= S[i] && S[i] <= '9')
            ret = ret * 10 + S[i] - '0';
    x = ret * f;
    return (is);
}
ostream &operator <<(ostream &os, __int128_t x) {
    ostream::sentry s(os);
    if (s) {
        __uint128_t tmp = x < 0 ? -x : x;
        char buffer[128]; char *d = end(buffer);
        do {
            --d; *d = "0123456789"[tmp % 10]; tmp /= 10;
        } while (tmp != 0);
        if (x < 0) { --d; *d = '-'; }
        int len = end(buffer) - d;
        if (os.rdbuf()->sputn(d, len) != len) os.setstate(ios_base::badbit);
    }
    return os;
}

__int128_t stoll(string &S) {
    __int128_t ret = 0; int f = 1;
    if (S[0] == '-') f = -1; 
    for (int i = 0; i < S.length(); i++)
        if ('0' <= S[i] && S[i] <= '9') ret = ret * 10 + S[i] - '0';
    return ret * f;
}
__int128_t gcd(__int128_t a, __int128_t b) { return b ? gcd(b, a % b) : a; }
__int128_t lcm(__int128_t a, __int128_t b) {
    return a / gcd(a, b) * b;
    // lcmが__int128_tに収まる必要あり
}

string to_string(ld x, int k) { // xの小数第k位までをstring化する
    assert(k >= 0);
    stringstream ss;
    ss << setprecision(k + 2) << x;
    string s = ss.str();
    if (s.find('.') == string::npos) s += '.';
    int pos = s.find('.');
    for (int i = 0; k >= (int)s.size() - 1 - pos; i++) s += '0';
    s.pop_back();
    if (s.back() == '.') s.pop_back();
    return s;

    // stringstream ss; // 第k+1位を四捨五入して第k位まで返す
    // ss << setprecision(k + 1) << x;
    // string s = ss.str();
    // if (s.find('.') == string::npos) s += '.';
    // int pos = s.find('.');
    // for (int i = 0; k > (int)s.size() - 1 - pos; i++) s += '0';
    // if (s.back() == '.') s.pop_back();
    // return s;
}
string to_string(__int128_t x) {
    string ret = "";
    if (x < 0) { ret += "-"; x *= -1; }
    while (x) { ret += (char)('0' + x % 10); x /= 10; }
    reverse(ret.begin(), ret.end());
    return ret;
}
string to_string(char c) { string s = ""; s += c; return s; }

template<class T> size_t HashCombine(const size_t seed,const T &v) {
    return seed^(hash<T>()(v)+0x9e3779b9+(seed<<6)+(seed>>2));
}
template<class T,class S> struct hash<pair<T,S>>{
    size_t operator()(const pair<T,S> &keyval) const noexcept {
        return HashCombine(hash<T>()(keyval.first), keyval.second);
    }
};
template<class T> struct hash<vector<T>>{
    size_t operator()(const vector<T> &keyval) const noexcept {
        size_t s=0;
        for (auto&& v: keyval) s=HashCombine(s,v);
        return s;
    }
};
template<int N> struct HashTupleCore{
    template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{
        size_t s=HashTupleCore<N-1>()(keyval);
        return HashCombine(s,get<N-1>(keyval));
    }
};
template <> struct HashTupleCore<0>{
    template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{ return 0; }
};
template<class... Args> struct hash<tuple<Args...>>{
    size_t operator()(const tuple<Args...> &keyval) const noexcept {
        return HashTupleCore<tuple_size<tuple<Args...>>::value>()(keyval);
    }
};

vector<mint> _fac, _finv, _inv;
void COMinit(int N) {
    _fac.resize(N + 1); _finv.resize(N + 1);  _inv.resize(N + 1);
    _fac[0] = _fac[1] = 1; _finv[0] = _finv[1] = 1; _inv[1] = 1;
    for (int i = 2; i <= N; i++) {
        _fac[i] = _fac[i-1] * mint(i);
        _inv[i] = -_inv[MOD % i] * mint(MOD / i);
        _finv[i] = _finv[i - 1] * _inv[i];
    }
}

mint FAC(int N) {
    if (N < 0) return 0; return _fac[N];
}
mint COM(int N, int K) {
    if (N < K) return 0; if (N < 0 or K < 0) return 0;
    return _fac[N] * _finv[K] * _finv[N - K];
}
mint PERM(int N, int K) {
    if (N < K) return 0; if (N < 0 or K < 0) return 0;
    return _fac[N] *  _finv[N - K];
}
mint NHK(int N, int K) { // initのサイズに注意
    if (N == 0 && K == 0)  return 1;
    return COM(N + K - 1, K);
}

#pragma endregion

vector<string> split_str(string S, char c) {
    vector<string> ret;
    stringstream ss;
    for (int i = 0; i < S.size(); i++) {
        if (S[i] == c) {
            ret.pb(ss.str());
            ss.str("");
            ss.clear();
        } else {
            ss << S[i];
        }
    }
    ret.pb(ss.str());
    return ret;
}

vector<int> erat(int N) {
    vector<bool> prime(N + 1, true);
    prime[0] = false;
    if (N >= 1) prime[1] = false;

    for (int i = 2; i * i <= N; i++) {
        if (prime[i]) {
            for (int j = i + i; j <= N; j += i) {
                prime[j] = false;
            }
        }
    }

    vector<int> ret;
    for (int i = 2; i <= N; i++) {
        if (prime[i]) ret.pb(i);
    }
    return ret;
}
signed main() {
    // string S;
    // unordered_map<string, int> mp;
    // while (cin >> S) {
    //     vector<string> V = split_str(S, ',');
    //     mp[V[1]]++;
    // }
    vector<int> P = erat(5e4);
    int sz = P.size();
    vector<int> dp(1e5 + 1);
    for (int i = 0; i < sz; i++) {
        for (int j = i; j < sz; j++) {
            dp[P[i] + P[j]]++;
        }
    }

    int x;
    while (cin >> x, x) {
        cout << dp[x] << endl;
    }
}
accuracy: 1
time_ms: 10
memory_kb: 4116
final_rank: 19

code_snippet: #include <iostream>
#include <vector>
using namespace std;

int main(void) {
  vector<int> isPrime(51000 + 1, false);
  isPrime[2] = true;
  for (int i = 3; i < 51000; i += 2) {
    isPrime[i] = true;
  }
  for (int i = 3; i*i < 51000; i += 2) {
    if (isPrime[i]) {
      for (int j = i * i; j < 51000; j += i) {
        isPrime[j] = false;
      }
    }
  }
  vector<int> primes;
  primes.reserve(51000/2); // Assuming half of the numbers are prime for upper limit
  primes.push_back(2);
  for (int i = 3; i < 51000; i += 2) {
    if (isPrime[i])
      primes.push_back(i);
  }
  int n;
  while (cin >> n && n != 0) {
    int kotae = 0;
    int i = 0, j = primes.size() - 1;
    while (i <= j) {
      if (primes[i] + primes[j] > n) {
        j--;
      } else if (primes[i] + primes[j] < n) {
        i++;
      } else {
        kotae++;
        i++;
        j--;
      }
    }
    cout << kotae << endl;
  }
  return 0;
}
accuracy: 1
time_ms: 110
memory_kb: 3096
final_rank: 11

code_snippet: #include <iostream>
#include <bitset>
#include <vector>
using namespace std;

#define MAX 51000

bitset<MAX + 1> isPrime;
vector<int> primes;

void generatePrimes() {
  isPrime.set(); // set all bits to 1
  isPrime[0] = isPrime[1] = false;
  primes.push_back(2);
  for (int i = 4; i <= MAX; i += 2)
    isPrime[i] = false;
  
  for (int i = 3; i * i <= MAX; i += 2) {
    if (isPrime[i]) {
      primes.push_back(i);
      for (int j = i * i; j <= MAX; j += i) {
        isPrime[j] = false;
      }
    }
  }
  for(int i = primes.back() + 2; i <= MAX; i += 2) {
    if(isPrime[i]) primes.push_back(i);
  }
}

int main(void) {
  generatePrimes();
  int n;
  while (cin >> n && n != 0) {
    int kotae = 0;
    for (int i = 0; i < primes.size() && primes[i] <= n / 2; i++) {
      if (isPrime[n - primes[i]])
        kotae++;
    }
    cout << kotae << endl;
  }
  return 0;
}
accuracy: 1
time_ms: 20
memory_kb: 3196
final_rank: 7

code_snippet: #include <iostream>
#include <vector>
using namespace std;

int main(void) {
  vector<int> isPrime(51000 + 1, 0);
  isPrime[2] = 1;
  for (int i = 3; i < 51000; i += 2) {
    isPrime[i] = 1;
  }

  // Start checking multiples from the square of each prime number
  for (int i = 3; i * i < 51000; i += 2) {
    if (isPrime[i]) {
      for (int j = i * i; j < 51000; j += i) {
        isPrime[j] = 0;
      }
    }
  }

  vector<int> primes;
  primes.push_back(2);
  for (int i = 3; i < 51000; i += 2) {
    if (isPrime[i])
      primes.push_back(i);
  }

  int n;
  while (cin >> n && n != 0) {
    int kotae = 0;
    // Limit prime number iteration
    for (int i = 0; primes[i] <= n / 2; i++) {
      if (isPrime[n - primes[i]])
        kotae++;
    }
    cout << kotae << endl;
  }
  return 0;
}
accuracy: 1
time_ms: 10
memory_kb: 3188
final_rank: 3

code_snippet: #include <iostream>
#include <vector>
#include <bitset>
using namespace std;

int main(void) {
  const int limit = 51000;
  bitset<limit + 1> isPrime;
  isPrime[2] = true;
  for (int i = 3; i <= limit; i += 2) {
    isPrime[i] = true;
  }
  for (int i = 3; i * i <= limit; i += 2) {
    if (isPrime[i]) {
      for (int j = i * i; j <= limit; j += i) {
        isPrime[j] = false;
      }
    }
  }
  vector<int> primes;
  primes.push_back(2);
  for (int i = 3; i <= limit; i += 2) {
    if (isPrime[i])
      primes.push_back(i);
  }
  int n;
  while (cin >> n && n != 0) {
    int kotae = 0;
    for (int i = 0; i < primes.size() && primes[i] <= n / 2; i++) {
      if (isPrime[n - primes[i]])
        kotae++;
    }
    cout << kotae << endl;
  }
  return 0;
}
accuracy: 1
time_ms: 20
memory_kb: 3128
final_rank: 2

code_snippet: #include <iostream>
#include <vector>
using namespace std;

int main(void) {
  int MAX = 51000;
  vector<bool> isPrime(MAX + 1, true); // Initialize all to true
  vector<int> primes;

  isPrime[0] = isPrime[1] = false; // 0 and 1 are not prime numbers
  primes.push_back(2); // Add 2 to the list of prime numbers

  // Sieve of Eratosthenes algorithm
  for (int i = 2; i * i <= MAX; i++) {
    if (isPrime[i]) {
      for (int j = i * i; j <= MAX; j += i) {
        isPrime[j] = false;
      }
    }
  }
  
  // Add prime numbers to the list
  for (int i = 3; i <= MAX; i += 2) {
    if (isPrime[i])
      primes.push_back(i);
  }

  int n;
  while (cin >> n && n != 0) {
    int kotae = 0;
    for (int i = 0; i < primes.size(); i++) {
      if (primes[i] <= n / 2) {
        if (isPrime[n - primes[i]]) // Use [] instead of at
          kotae++;
      }
    }
    cout << kotae << endl;
  }
  return 0;
}
accuracy: 1
time_ms: 40
memory_kb: 3180
final_rank: 9

code_snippet: #include <iostream>
#include <vector>
using namespace std;

int main(void) {
  const int limit = 51000;
  vector<bool> isPrime(limit + 1, true);
  isPrime[0] = isPrime[1] = false;

  for (int i = 2; i * i <= limit; i++) {
    if (isPrime[i]) {
      for (int j = i * i; j <= limit; j += i) {
        isPrime[j] = false;
      }
    }
  }
  
  vector<int> primes;
  for (int i = 2; i <= limit; i++) {
    if (isPrime[i])
      primes.push_back(i);
  }
  
  int n;
  while (cin >> n && n != 0) {
    int kotae = 0;
    for (int i = 0; i < primes.size() && primes[i] <= n/2; i++) {
      if (isPrime[n - primes[i]])
        kotae++;
    }
    cout << kotae << endl;
  }
  
  return 0;
}
accuracy: 1
time_ms: 20
memory_kb: 3216
final_rank: 8

code_snippet: #include <iostream>
#include <vector>
#include <cmath>
using namespace std;
int main(void) {
  int limit = 51000;
  vector<char> isPrime(limit + 1, true);
  isPrime[0] = isPrime[1] = false;
  int sqrt_limit = sqrt(limit);
  
  for (int i = 2; i <= sqrt_limit; i++) {
    if (isPrime[i]) {
      for (int j = i * i; j <= limit; j += i) {
        isPrime[j] = false;
      }
    }
  }
  
  vector<int> primes;
  if(limit >= 2) primes.push_back(2);
  for (int i = 3; i <= limit; i += 2) {
    if (isPrime[i])
      primes.push_back(i);
  }

  int n;
  while (cin >> n && n != 0) {
    int kotae = 0;
    for (int i = 0; i < primes.size() && primes[i] <= n / 2; i++) {
      if (isPrime[n - primes[i]])
        kotae++;
    }
    cout << kotae << endl;
  }
  return 0;
}
accuracy: 1
time_ms: 10
memory_kb: 3220
final_rank: 5

code_snippet: #include <iostream>
#include <bitset>
using namespace std;
int main(void) {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  
  bitset<51000 + 1> isPrime;
  isPrime[2] = true;
  for (int i = 3; i <= 51000; i += 2) {
    isPrime[i] = true;
  }
  for (int i = 3; i * i <= 51000; i += 2) {
    if (isPrime[i]) {
      for (int j = i * i; j <= 51000; j += i) {
        isPrime[j] = false;
      }
    }
  }
  int n;
  while (cin >> n && n != 0) {
    int kotae = 0;
    for (int i = 2; i <= n / 2; i++) {
      if (isPrime[i] && isPrime[n - i])
        kotae++;
    }
    cout << kotae << '\n';
  }
  return 0;
}
accuracy: 1
time_ms: 180
memory_kb: 3176
final_rank: 16

code_snippet: #include <iostream>
#include <vector>
#include <bitset>
#include <cmath>
using namespace std;

int main() {
  const int limit = 51000;
  bitset<limit + 1> isPrime;
  isPrime.set();
  isPrime[0] = isPrime[1] = false;

  for (int i = 2; i * i <= limit; i++) {
    if (isPrime[i]) {
      for (int j = i * i; j <= limit; j += i) {
        isPrime[j] = false;
      }
    }
  }

  vector<int> primes;
  for (int i = 2; i <= limit; i++) {
    if (isPrime[i]) {
      primes.push_back(i);
    }
  }

  int n;
  while (cin >> n && n != 0) {
    int kotae = 0;
    int left = 0, right = primes.size() - 1;
    while (left <= right) {
      int sum = primes[left] + primes[right];
      if (sum == n) {
        kotae++;
        left++;
        right--;
      } else if (sum < n) {
        left++;
      } else {
        right--;
      }
    }
    cout << kotae << endl;
  }

  return 0;
}
accuracy: 1
time_ms: 110
memory_kb: 3136
final_rank: 12

code_snippet: #include <iostream>
#include <vector>
#include <cmath>
using namespace std;

int main(void) {
  vector<bool> isPrime(51000 + 1, false);
  isPrime[2] = true;
  for (int i = 3; i < 51000; i += 2) {
    isPrime[i] = true;
  }

  int limit = sqrt(51000);
  for (int i = 3; i <= limit; i += 2) {
    if (isPrime[i]) {
      for (int j = i*i; j < 51000; j += i) {
        isPrime[j] = false;
      }
    }
  }

  int n;
  while (cin >> n && n != 0) {
    int count = 0;
    for (int i = 2; i <= n / 2; ++i) {
      if (isPrime[i] && isPrime[n - i]) {
        count++;
      }
    }
    cout << count << endl;
  }
  return 0;
}
accuracy: 1
time_ms: 190
memory_kb: 3084
final_rank: 15

code_snippet: #include <iostream>
#include <vector>
using namespace std;

int main(void) {
    const int maxNum = 51000;
    vector<bool> isPrime(maxNum + 1, false);
    isPrime[2] = true;
    for (int i = 3; i <= maxNum; i += 2) {
        isPrime[i] = true;
    }
    for (int i = 3; i <= maxNum; i += 2) {
        if (isPrime[i]) {  // Only check for prime numbers
            for (int j = i + i; j <= maxNum; j += i) {
                isPrime[j] = false;
            }
        }
    }
    vector<int> primes;
    primes.reserve(maxNum/2);  // Preallocate memory
    primes.push_back(2);
    for (int i = 3; i <= maxNum; i += 2) {
        if (isPrime[i]) {
            primes.push_back(i);
        }
    }
    int n;
    while (cin >> n && n != 0) {
        int kotae = 0;
        for (int i = 0; i < primes.size() && primes[i] <= n / 2; i++) {
            if (isPrime[n - primes[i]]) {
                kotae++;
            }
        }
        cout << kotae << endl;
    }
    return 0;
}
accuracy: 1
time_ms: 20
memory_kb: 3108
final_rank: 1

code_snippet: #include <iostream>
#include <vector>
#include <cmath>
using namespace std;
int main(void) {
  vector<bool> isPrime(51000 + 1, true);
  vector<int> primes;
  primes.reserve(51000); // Reserve memory in advance
  isPrime[0] = isPrime[1] = false;
  for (int i = 2; i*i <= 51000; i++) {
    if (isPrime[i]) {
      for (int j = i*i; j <= 51000; j += i) {
        isPrime[j] = false;
      }
    }
  }
  for (int i = 2; i <= 51000; i++) {
    if (isPrime[i])
      primes.push_back(i);
  }
  int n;
  int size = primes.size(); // Store size in a variable
  while (cin >> n && n != 0) {
    int kotae = 0;
    for (int i = 0; i < size; i++) {
      if (primes[i] <= n / 2) {
        if (isPrime[n - primes[i]]) // Use operator [] instead of at()
          kotae++;
      }
    }
    cout << kotae << endl;
  }
  return 0;
}
accuracy: 1
time_ms: 40
memory_kb: 3060
final_rank: 4

code_snippet: #include <iostream>
#include <vector>
#include <cmath>
using namespace std;

int main(void) {
  vector<bool> isPrime(51000 + 1, true);
  isPrime[0] = isPrime[1] = false;
  for (int i = 2; i <= sqrt(51000); i++) {
    if (isPrime[i]) {
      for (int j = i * i; j <= 51000; j += i) {
        isPrime[j] = false;
      }
    }
  }
  int n;
  while (cin >> n && n != 0) {
    int kotae = 0;
    for (int i = 2; i <= n / 2; i++) {
      if (isPrime[i] && isPrime[n - i])
        kotae++;
    }
    cout << kotae << endl;
  }
  return 0;
}
accuracy: 1
time_ms: 200
memory_kb: 2992
final_rank: 14

code_snippet: #include <iostream>
#include <vector>
using namespace std;

int main() {
  const int limit = 51000;
  vector<bool> isPrime(limit + 1, true);
  isPrime[0] = isPrime[1] = false;
  
  for (int i = 2; i*i <= limit; i++) {
    if (isPrime[i]) {
      for (int j = i*i; j <= limit; j += i) {
        isPrime[j] = false;
      }
    }
  }

  int n;
  while (cin >> n && n != 0) {
    int count = 0;
    for (int i = 2; i <= n / 2; i++) {
      if (isPrime[i] && isPrime[n - i]) {
        count++;
      }
    }
    cout << count << endl;
  }
  return 0;
}
accuracy: 1
time_ms: 210
memory_kb: 3092
final_rank: 18

code_snippet: #include <iostream>
#include <vector>
using namespace std;
int main(void) {
  vector<bool> isPrime(51000 + 1, true);
  isPrime[0] = isPrime[1] = false;
  for (int i = 2; i * i <= 51000; i++) {
    if (isPrime[i]) {
      for (int j = i * i; j <= 51000; j += i) {
        isPrime[j] = false;
      }
    }
  }
  int n;
  while (cin >> n && n != 0) {
    int kotae = 0;
    for (int i = 2; i <= n / 2; i++) {
      if (isPrime[i] && isPrime[n - i])
        kotae++;
    }
    cout << kotae << endl;
  }
  return 0;
}
accuracy: 1
time_ms: 210
memory_kb: 3056
final_rank: 17

code_snippet: #include <iostream>
#include <bitset>
using namespace std;
int main(void) {
  ios::sync_with_stdio(false);
  bitset<51001> isPrime;
  isPrime.set();
  isPrime[0] = isPrime[1] = 0;
  for (int i = 4; i <= 51000; i += 2) {
    isPrime[i] = 0;
  }
  for (int i = 3; i * i <= 51000; i += 2) {
    if (isPrime[i]) {
      for (int j = i * i; j <= 51000; j += i) {
        isPrime[j] = 0;
      }
    }
  }
  int n;
  while (cin >> n && n != 0) {
    int kotae = 0;
    for (int i = 2; i <= n / 2; ++i) {
      if (isPrime[i] && isPrime[n - i])
        kotae++;
    }
    cout << kotae << "\n";
  }
  return 0;
}
accuracy: 1
time_ms: 180
memory_kb: 3024
final_rank: 13

code_snippet: #include <iostream>
#include <bitset>
#include <vector>
#include <cmath>
using namespace std;

int main(void) {
  const int limit = 51000;
  const int sqrtLimit = sqrt(limit);

  bitset<limit + 1> isPrime;
  isPrime[2] = true;
  for (int i = 3; i <= limit; i += 2) {
    isPrime[i] = true;
  }
  for (int i = 3; i <= sqrtLimit; i += 2) {
    if (isPrime[i]) {
      for (int j = i * i; j <= limit; j += i * 2) {
        isPrime[j] = false;
      }
    }
  }

  vector<int> primes;
  primes.push_back(2);
  for (int i = 3; i <= limit; i += 2) {
    if (isPrime[i])
      primes.push_back(i);
  }

  int n;
  while (cin >> n && n != 0) {
    int kotae = 0;
    int primesSize = primes.size();
    for (int i = 0; i < primesSize; i++) {
      if (primes[i] <= n / 2) {
        if (isPrime[n - primes[i]])
          kotae++;
      }
    }
    cout << kotae << endl;
  }

  return 0;
}
accuracy: 1
time_ms: 40
memory_kb: 3192
final_rank: 10

code_snippet: #include <iostream>
#include <vector>
using namespace std;

int main(void) {
  vector<char> isPrime(51000 + 1, false);
  isPrime[2] = true;

  for (int i = 3; i < 51000; i += 2) {
    isPrime[i] = true;
  }

  for (int i = 3; i < 51000; i += 2) {
    if (isPrime[i]) {
      for (int j = i + i; j < 51000; j += i) {
        isPrime[j] = false;
      }
    }
  }

  vector<int> primes;
  primes.push_back(2);

  for (int i = 3; i < 51000; i += 2) {
    if (isPrime[i]) {
      primes.push_back(i);
    }
  }

  int n;
  while (cin >> n && n != 0) {
    int kotae = 0;
    int maxSize = n / 2;
    int left = 0;
    int right = primes.size() - 1;
    int lastIndex = -1;

    while (left <= right) {
      int mid = left + (right - left) / 2;

      if (primes[mid] <= maxSize) {
        lastIndex = mid;
        left = mid + 1;
      } else {
        right = mid - 1;
      }
    }

    for (int i = 0; i <= lastIndex; i++) {
      if (isPrime[n - primes[i]]) {
        kotae++;
      }
    }

    cout << kotae << endl;
  }

  return 0;
}
accuracy: 1
time_ms: 20
memory_kb: 3188
final_rank: 6