#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <iostream>
#include <string>
#include <cstdlib>
#include <cmath>
#include <vector>
#include <unordered_map>
#include <map>
#include <set>
#include <algorithm>
#include <queue>
#include <stack>
#include <functional>
#include <bitset>
#include <assert.h>
#include <unordered_map>
#include <fstream>
#include <ctime>
#include <complex>
using namespace std;
typedef long long ll;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<char> vc;
typedef vector<string> vs;
typedef vector<bool> vb;
typedef vector<double> vd;
typedef pair<ll,ll> P;
typedef pair<int,int> pii;
typedef vector<P> vpl;
typedef tuple<ll,ll,ll> tapu;
#define rep(i,n) for(int i=0; i<(n); i++)
#define REP(i,a,b) for(int i=(a); i<(b); i++)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
const int inf = 1<<30;
const ll linf = 1LL<<62;
const int MAX = 510000;
ll dy[8] = {1,-1,0,0,1,-1,1,-1};
ll dx[8] = {0,0,1,-1,1,-1,-1,1};
const double pi = acos(-1);
const double eps = 1e-10;
template<typename T1,typename T2> inline bool chmin(T1 &a,T2 b){
	if(a>b){
		a = b; return true;
	}
	else return false;
}
template<typename T1,typename T2> inline bool chmax(T1 &a,T2 b){
	if(a<b){
		a = b; return true;
	}
	else return false;
}
template<typename T> inline void print(T &a){
    for(auto itr = a.begin(); itr != a.end(); itr++){
		cout << *itr << " ";
	}
    cout << "\n";
}
template<typename T1,typename T2> inline void print2(T1 a, T2 b){
	cout << "debug: " << a << " " << b << "\n";
}
template<typename T1,typename T2,typename T3> inline void print3(T1 a, T2 b, T3 c){
	cout << "debug: " << a << " " << b << " " << c << "\n";
}
void mark() {cout << "#" << "\n";}
ll pcount(ll x) {return __builtin_popcountll(x);}
const int mod = 1e9 + 7;
//const int mod = 998244353;

ll phi(ll n){
	ll res = n;
	for(ll i=2; i*i<=n; i++){
		if(n % i == 0){
			res /= i; res *= i-1;
		}
		while(n % i == 0){
			n /= i;
		}
	}
	if(n != 1){
		res /= n; res *= n-1;
	}
	return res;
}

vl divisor(ll k){
	vl c;
	for(ll i=1; i*i<=k; i++){
		if(k % i == 0){
			c.push_back(i);
			if((k / i) != i){
				c.push_back(k/i);
			}
		}
	}
	sort(c.begin(), c.end());
	return c;
}

ll modpow(ll x, ll n, ll mod){
	ll res = 1;
	while(n > 0){
		if(n & 1) res = res * x % mod;
		x = x * x % mod;
		n >>= 1;
	}
	return res;
}

int main(){
	int t; cin >> t;
	while(t--){
		ll n; cin >> n;
		if(n == 1){
			cout << 1 << "\n";
			continue;
		}
		vl div = divisor(phi(2*n-1));
		for(auto i : div){
			if(modpow(2,i,2*n-1) == 1){
				cout << i << "\n";
				break;
			}
		}
	}
}