#include #include typedef long long int ll; using namespace std; typedef pair P; using namespace atcoder; template using min_priority_queue = priority_queue, greater>; #define USE998244353 #ifdef USE998244353 const ll MOD = 998244353; using mint = modint998244353; #else const ll MOD = 1000000007; using mint = modint1000000007; #endif #pragma region //使いがち const int MAX = 2000001; long long fac[MAX], finv[MAX], inv[MAX]; void COMinit() { fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (int i = 2; i < MAX; i++){ fac[i] = fac[i - 1] * i % MOD; inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD; finv[i] = finv[i - 1] * inv[i] % MOD; } } long long COM(int n, int k){ if (n < k) return 0; if (n < 0 || k < 0) return 0; return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD; } ll gcd(ll x, ll y) { if (y == 0) return x; else if (y > x) { return gcd (y, x); } else return gcd(x % y, y); } ll lcm(ll x, ll y) { return x / gcd(x, y) * y; } ll my_sqrt(ll x) { ll m = 0; ll M = 3000000001; while (M - m > 1) { ll now = (M + m) / 2; if (now * now <= x) { m = now; } else { M = now; } } return m; } ll pow_ll(ll x, ll n) { if (n == 0) return 1; if (n % 2) { return pow_ll(x, n - 1) * x; } else { ll tmp = pow_ll(x, n / 2); return tmp * tmp; } } ll keta(ll num, ll arity) { ll ret = 0; while (num) { num /= arity; ret++; } return ret; } // k進数で見た時のi桁目の数を返す (一番下は0桁目) ll keta_num(ll num, ll i, ll k) { return (num / pow_ll(k, i)) % k; } ll ceil(ll n, ll m) { // n > 0, m > 0 ll ret = n / m; if (n % m) ret++; return ret; } void compress(vector& v) { // [3 5 5 6 1 1 10 1] -> [1 2 2 3 0 0 4 0] vector u = v; sort(u.begin(), u.end()); u.erase(unique(u.begin(),u.end()),u.end()); map mp; for (int i = 0; i < u.size(); i++) { mp[u[i]] = i; } for (int i = 0; i < v.size(); i++) { v[i] = mp[v[i]]; } } // N以下の素数を全て返す vector Eratosthenes( const ll N ) { vector is_prime( N + 1 ); for( ll i = 0; i <= N; i++ ) { is_prime[ i ] = true; } vector P; for( ll i = 2; i <= N; i++ ) { if( is_prime[ i ] ) { for( ll j = 2 * i; j <= N; j += i ) { is_prime[ j ] = false; } P.emplace_back( i ); } } return P; } vector > prime_factorize(ll N) { vector > res; for (ll a = 2; a * a <= N; ++a) { if (N % a != 0) continue; ll ex = 0; // 指数 // 割れる限り割り続ける while (N % a == 0) { ++ex; N /= a; } // その結果を push res.push_back({a, ex}); } // 最後に残った数について if (N != 1) res.push_back({N, 1}); return res; } #pragma endregion // 1回しか出てこない素数はどうでもいい vector > prime_factorize_here(ll N) { vector > res; for (ll a = 2; a * a * a <= N; ++a) { if (N % a != 0) continue; ll ex = 0; // 指数 // 割れる限り割り続ける while (N % a == 0) { ++ex; N /= a; } // その結果を push res.push_back({a, ex}); } if (N == 1) return res; if (my_sqrt(N) * my_sqrt(N) == N) { res.push_back({my_sqrt(N), 2}); } return res; } // 0 <= a_1 <= a_2 <= ... <= a_n , a_1 + a_2 + ... + a_n = Sとなる場合のかず // n, Sは最大で60 // dp[i][j][k] := i番目まで見て、最後の数がjで、和がkになる場合の数 ll solve(ll n, ll s) { vector>> dp(n + 1, vector>(s + 1, vector(s + 1, 0))); dp[0][0][0] = 1; for (int i = 0; i < n; i++) { for (int j = 0; j <= s; j++) { for (int k = 0; k <= s; k++) { for (int l = max(1, j); l <= s; l++) { int ni = i + 1; int nj = l; int nk = k + l; if (nk > s) continue; dp[ni][nj][nk] += dp[i][j][k]; } } } } ll ret = 0; for (int i = 0; i <= n; i++) { for (int j = 0; j <= s; j++) { ret += dp[i][j][s]; } } return ret; } int main() { ll n; cin >> n; auto p = prime_factorize(n); ll ans = 1; for (auto x : p) { ans *= solve(60, x.second); } cout << ans << endl; return 0; }