#include <iostream>

using namespace std;
int phi(int x){
    int eu = x;
    for(int i=2;i*i<=x;i++){
        if(x%i==0){
            eu /= i; eu *= (i - 1);
        }
        while(x%i==0) x /= i;
    }
    if(x!=1){
        eu /= x; eu *= (x - 1);
    }
    return eu;
}
bool solve(int a,int x,int mod){
    int ret = 1;
    while(x){
        if(x&1) (ret *= a) %= mod;
        (a *= a) %= mod; x /= 2;
    }
    return ret==1;
}

int main(){
    int t; cin >> t;
    while(t){
        t--;
        int i,n; cin >> n;
        n = 2*n - 1;
        int m = phi(n);
        int ans = m;
        if(n==1){
            cout << 1 << endl;
        }else{
            for(i=1;i*i<=m;i++){
                if(m%i==0){
                    if(solve(2,i,n)) ans = min(ans,i);
                    if(solve(2,m/i,n)) ans = min(ans,m/i);
                }
            }
            cout << ans << endl;
        }
    }
}