#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <set>
#include <map>

using namespace std;
typedef long long ll;

template <typename T>
vector<T> prime_facs(T N) {
	vector<T> ans;
	for (int i = 2; i * i <= N; i++) {
		if (N % i == 0) {
		ans.push_back(i);
            while (N % i == 0) {
                N /= i;
            }
		}
	}
	if (N != 1) ans.push_back(N);
	return ans;
}

template <typename T>
T pow(T a, ll n, ll MOD) {
	T ans = 1;
	T tmp = a;
	for (int i = 0; i <= 60; i++) {
		ll m = (ll)1 << i;
		if (m & n) {
		ans *= tmp;
		ans %= MOD;
		}
		tmp *= tmp;
		tmp %= MOD;
	}
	return ans;
}

template <typename T>
vector<T> divs(T N) {
	vector<T> ans;
	for (int i = 1; i * i <= N; i++) {
		if (N % i == 0) {
		ans.push_back(i);
		if (i * i != N) ans.push_back(N / i);
		}
	}
	return ans;
}

void solve(){
    int n; cin >> n;
    if(n == 1) {
        cout << 1 << endl;
        return;
    }
    auto v = prime_facs<int>(2*n-1);
    int m = 2*n-1;
    for(int i : v){
        m = (m/i)*(i-1);
    }
    auto u = divs<int>(m);
    sort(u.begin(), u.end());
    for(int k : u){
        if(pow<ll>(2, k, 2*n-1) == 1){
            cout << k << endl;
            return;
        }
    }
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    int t; cin >> t;
    for(int i = 0; i < t; i++) solve();
}