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| #pragma GCC optimize("Ofast")
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define gc()(is==it?it=(is=in)+fread(in,1,Q,stdin),(is==it?EOF:*is++):*is++)
const int Q = (1 << 24) + 1;
char in[Q], *is=in, *it=in, c;
void read(int &n){
for(n = 0; (c = gc()) < '0' || c > '9';);
for(; c <= '9' && c >= '0'; c = gc()) n = n * 10 + c - 48;
}
void read(ll &n){
for(n = 0; (c = gc()) < '0' || c > '9';);
for(; c <= '9' && c >= '0'; c = gc()) n = n * 10 + c - 48;
}
const int S = 8, modp = 998244353;
mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
ll rng(ll l, ll r){
uniform_int_distribution<ll> uni(l, r);
return uni(mt);
}
ll mult_mod(ll a, ll b, ll c){
a %= c;
b %= c;
ll ret = 0;
ll tmp = a;
while(b){
if(b & 1){
ret += tmp;
if(ret > c) ret -= c;
}
tmp <<= 1;
if(tmp > c) tmp -= c;
b >>= 1;
}
return ret;
}
ll pow_mod(ll a, ll n, ll mod){
ll ret = 1;
ll temp = a % mod;
while(n){
if(n & 1) ret = mult_mod(ret, temp, mod);
temp = mult_mod(temp, temp, mod);
n >>= 1;
}
return ret;
}
bool check(ll a, ll n, ll x, ll t){
ll ret = pow_mod(a, x, n);
ll last = ret;
for(int i = 1; i <= t; i++){
ret = mult_mod(ret, ret, n);
if(ret == 1 && last != 1 && last != n - 1) return true;
last = ret;
}
if(ret != 1) return true;
return false;
}
bool Miller_Rabin(ll n){
if(n < 2) return false;
if(n == 2) return true;
if((n & 1) == 0) return false;
ll x = n - 1;
ll t = 0;
while((x & 1) == 0){
x >>= 1;
t++;
}
for(int i = 0; i < S; i++){
ll a = rng(1, n - 1);
if(check(a, n, x, t)) return false;
}
return true;
}
ll factor[105], fac[105];
int tol, tot;
ll gcd(ll a, ll b){
ll t;
while(b){
t = a;
a = b;
b = t % b;
}
if(a >= 0) return a;
return -a;
}
ll pollard_rho(ll x, ll c){
ll i = 1, k = 2;
ll x0 = rng(1, x - 1);
ll y = x0;
while(true){
i++;
x0 = (mult_mod(x0, x0, x) + c) % x;
ll d = gcd(y - x0, x);
if(d != 1 && d != x) return d;
if(y == x0) return x;
if(i == k){
y = x0;
k += k;
}
}
}
void findfac(ll n, int k){
if(n == 1) return;
if(tol >= 1) return;
if(Miller_Rabin(n)){
factor[tol++] = n;
return;
}
ll p = n;
int c = k;
while(p >= n) p = pollard_rho(p, c--);
findfac(p, k);
findfac(n / p, k);
}
ll n;
ll qpow(ll a, ll b){
ll res = 1;
while(b){
if(b & 1) res = res * a;
b >>= 1;
a = a * a;
}
return res;
}
void solve(){
cin >> n;
if(n == 1){
cout << "1\n";
return;
}
for(int i = 1; i <= 60; i++){
ll x = powl(n, 1. / i);
for(int j = -1; j <= 1; j++){
ll y = x + j;
if(y < 2) continue;
if(qpow(y, i) == n && Miller_Rabin(y)){
cout << y % modp << '\n';
return;
}
}
}
cout << "1\n";
}
int main(){
int T = 1;
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
cin >> T;
while(T--) solve();
return 0;
}
|