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| #include <iostream>
#include <unordered_map>
#include <functional>
using i64 = long long;
const int mod = 998244353;
i64 quickPow(i64 x, i64 n, i64 mod) {
i64 res = 1;
while (n) {
if (n & 1) res = (__int128_t)res * x % mod;
x = (__int128_t)x * x % mod;
n >>= 1;
}
return res;
}
bool millerRabin(i64 n, int test_times = 8) {
if (n < 3 || n % 2 == 0) return n == 2;
i64 u = n - 1;
int t = 0;
while (!(u & 1)) {
u >>= 1;
t++;
}
for (int i = 0; i < test_times; i++) {
i64 a = std::rand() % (n - 2) + 2;
i64 v = quickPow(a, u, n);
if (v == 1) continue;
int s;
for (s = 0; s < t; s++) {
if (v == n - 1) break;
v = (__int128_t)v * v % n;
}
if (s == t) return false;
}
return true;
}
i64 gcd(i64 x, i64 y) {
return y == 0 ? x : gcd(y, x % y);
}
i64 Pollard_Rho(i64 x) {
i64 s = 0, t = 0;
i64 c = (i64)std::rand() % (x - 1) + 1;
int step = 0, goal = 1;
i64 val = 1;
for (goal = 1; ; goal <<= 1, s = t, val = 1) {
for (step = 1; step <= goal; step++) {
t = ((__int128_t)t * t + c) % x;
val = (__int128_t)val * std::abs(t - s) % x;
if (step % 127 == 0) {
i64 d = gcd(val, x);
if (d > 1) return d;
}
}
i64 d = gcd(val, x);
if (d > 1) return d;
}
}
i64 solve() {
i64 x;
std::cin >> x;
std::unordered_map<i64, int> res;
std::function<void(i64)> fac = [&res, &fac](i64 n) {
if (n < 2) return;
if (millerRabin(n)) {
res[n]++;
return;
}
i64 p = n;
while (p >= n) p = Pollard_Rho(n);
fac(p), fac(n / p);
};
fac(x);
if (res.size() == 1) {
return res.begin()->first;
}
else {
return 1;
}
}
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout.tie(nullptr);
int numTest;
std::cin >> numTest;
for (int i = 0; i < numTest; i++) {
std::cout << solve() % mod << " \n"[i == numTest - 1];
}
return 0;
}
|