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| using i128 = __int128_t;
const ll MOD = 998244353;
constexpr int MX = 1e5 + 1;
ll F[MX]; // 预处理阶乘
ll INV_F[MX]; // 预处理逆元
ll qpow(ll x, int n) {
ll res = 1;
for (; n; n >>= 1) {
if (n % 2) res = res * x % MOD;
x = x * x % MOD;
}
return res;
}
auto init = [] {
F[0] = 1;
for (int i = 1; i < MX; i++) F[i] = F[i - 1] * i % MOD; // 预处理阶乘
INV_F[MX - 1] = qpow(F[MX - 1], MOD - 2);
for (int i = MX - 1; i; i--) {
INV_F[i - 1] = INV_F[i] * i % MOD;
} // 预处理逆元
return 0;
}();
// 计算C(n,m),即从n个数中取m个数
ll comb(int n, int m) { return m < 0 || m > n ? 0 : F[n] * INV_F[m] % MOD * INV_F[n - m] % MOD; }
void solve() {
ll n;
cin >> n;
vector<pll> tem;
ll nn = n;
for (ll i = 2; i * i <= n; i++) {
if (nn % i == 0) {
ll tem2 = 0;
while (nn % i == 0) {
tem2++;
nn /= i;
}
tem.emplace_back(i, tem2);
}
}
if (nn > 1) tem.emplace_back(nn, 1);
vl tem2;
tem2.push_back(1);
for (auto& [x, y] : tem) {
int tem3 = sz(tem2);
ll tem4 = 1;
rep(j, 1, y) {
tem4 *= x;
rep(v, 0, tem3 - 1) tem2.push_back(tem2[v] * tem4);
}
}
ranges::sort(tem2);
int m = sz(tem2);
map<ll, ll> ma;
rep(i, 0, m - 1) { ma[tem2[i]] = i; }
vvl dp(m, vl(100));
vvl dp2(m, vl(100));
dp[0][0] = 1;
rep(i, 1, m - 1) {
frep(j, m - 1, 0) {
if ((i128)tem2[j] * tem2[i] > (i128)n) continue;
if (n % (tem2[j] * tem2[i]) != 0) continue;
frep(v, 98, 0) {
if (!dp[j][v]) continue;
dp[ma[tem2[j] * tem2[i]]][v + 1] = (dp[ma[tem2[j] * tem2[i]]][v + 1] + dp[j][v]) % MOD;
dp2[ma[tem2[j] * tem2[i]]][v + 1] =
(dp2[ma[tem2[j] * tem2[i]]][v + 1] + dp2[j][v] + dp[j][v] * (tem2[i] % MOD) % MOD) % MOD;
}
}
}
ll ans = 0;
rep(i, 0, 99) {
if (!dp[ma[n]][i]) continue;
ans = (ans + F[i + 1] * (dp[ma[n]][i] + dp2[ma[n]][i]) % MOD) % MOD;
if (i > 0) ans = (ans + F[i] * dp2[ma[n]][i] % MOD) % MOD;
}
cout << ans << endl;
return;
}
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