#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
typedef pair<ll, ll> p_ll;

template<class T>
void debug(T itr1, T itr2) { auto now = itr1; while(now<itr2) { cout << *now << " "; now++; } cout << endl; }
#define repr(i,from,to) for (ll i=(ll)from; i<(ll)to; i++)
#define all(vec) vec.begin(), vec.end()
#define rep(i,N) repr(i,0,N)
#define per(i,N) for (int i=(int)N-1; i>=0; i--)

const ll MOD = pow(10,9)+7;
const ll LLINF = pow(2,61)-1;
const int INF = pow(2,30)-1;

vector<ll> fac;
void c_fac(int x=pow(10,6)+10) { fac.resize(x,true); rep(i,x) fac[i] = i ? (fac[i-1]*i)%MOD : 1; }
ll modpow(ll x, ll p, ll m=MOD) { ll result = 1, now = 1, pm = x; while (now<=p) { if (p&now) { result = result * pm % m; } now*=2; pm = pm*pm % m; } return result; }
ll inv(ll a, ll m=MOD) { ll b = m, x = 1, y = 0; while (b!=0) { int d = a/b; a -= b*d; swap(a,b); x -= y*d; swap(x,y); } return (x+m)%m; }
ll nck(ll n, ll k) { return fac[n]*inv(fac[k]*fac[n-k]%MOD)%MOD; }
ll gcd(ll a, ll b) { if (a<b) swap(a,b); return b==0 ? a : gcd(b, a%b); }
ll lcm(ll a, ll b) { return a/gcd(a,b)*b; }


int main() {
  ll T; cin >> T;
  rep(_,T) {
    ll N; cin >> N;
    ll so = 1, tn = 2*N-1;
    for (ll i=2; i*i<=tn; i++) {
      if (tn%i==0) {
        ll count = 0; while (tn%i==0) { count++; tn/=i; }
        so *= modpow(i,count-1) * (i-1);
      }
    }
    if (tn!=1) so *= tn-1;

    vector<ll> yaku; for (ll i=1; i*i<=so; i++) if (so%i==0) { yaku.push_back(i); yaku.push_back(so/i); }
    sort(all(yaku));
    for (auto x: yaku) {
      if (modpow(2,x,2*N-1)==1) { cout << x << endl; break; }
    }
  }
  // cout << result << endl;
  return 0;
}