#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < n; i++)
#define rep2(i, x, n) for(int i = x; i <= n; i++)
#define rep3(i, x, n) for(int i = x; i >= n; i--)
#define elif else if
#define sp(x) fixed << setprecision(x)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
const int MOD = 1000000007;
//const int MOD = 998244353;
const int inf = (1<<30)-1;
const ll INF = (1LL<<60)-1;
const double pi = acos(-1.0);
const double EPS = 1e-10;
template<typename T> bool chmax(T &x, const T &y) {return (x < y)? (x = y, true) : false;};
template<typename T> bool chmin(T &x, const T &y) {return (x > y)? (x = y, true) : false;};

struct Random_Number_Generator{
    mt19937_64 mt;

    Random_Number_Generator() : mt(chrono::steady_clock::now().time_since_epoch().count()) {}

    int64_t operator () (int64_t l, int64_t r){
        uniform_int_distribution<int64_t> dist(l, r-1);
        return dist(mt);
    }

    int64_t operator () (int64_t r){ 
        return (*this)(0, r);
    }
};

template<typename T>
struct Modulo{
    Modulo() {};

    T pow(T x, ll n, const T &m) const{
        T ret = 1;
        while(n){
            if(n&1) ret *= x, ret %= m;
            x *= x, x %= m;
            n >>= 1;
        }
        return ret;
    }

    T Euler_Totient(T m) const{ //オイラーのφ関数(xとmが互いに素ならば、x^φ(m)≡1(mod m))
        T ret = m;
        for(T i = 2; i*i <= m; i++){
            if(m%i == 0) ret *= i-1, ret /= i;
            while(m%i == 0) m /= i;
        }
        if(m > 1) ret *= m-1, ret /= m;
        return ret;
    }

    T log(const T &x, T y, const T &m) const{ //x^k=y(mod m)となる最小の非負整数k(xとmは互いに素)
        unordered_map<T, T> mp;
        T n = 0, now = 1;
        for(; n*n < m; n++){
            if(!mp.count(now)) mp[now] = n;
            now *= x, now %= m;
        }
        now = pow(now, Euler_Totient(m)-1, m);
        rep(i, n){
            if(mp.count(y) && n*i+mp[y] > 0) return n*i+mp[y];
            y *= now, y %= m;
        }
        return -1;
    }

    T primitive_root(T m){ //素数mの原始根
        vector<T> ds;
        for(T i = 1; i*i <= m-1; i++){
            if((m-1)%i == 0) ds.pb(i), ds.pb((m-1)/i);
        }
        sort(all(ds));
        Random_Number_Generator rnd;
        while(true){
            T r = rnd(1, m);
            for(auto &e: ds){
                if(e == m-1) return r;
                if(pow(r, e, m) == 1) break;
            }
        }
    }
};

template<typename T>
struct Prime{
    Prime() {}

    vector<T> divisors(const T &n) const{
        vector<T> ret;
        for(T i = 1; i*i <= n; i++){
            if(n%i == 0){
                ret.pb(i);
                if(i*i != n) ret.pb(n/i);
            }
        }
        //sort(all(ret));
        return ret;
    }

    vector<pair<T, int>> prime_factor(T n) const{
        vector<pair<T, int>> ret;
        for(T i = 2; i*i <= n; i++){
            int cnt = 0;
            while(n%i == 0) cnt++, n /= i;
            if(cnt > 0) ret.eb(i, cnt);
        }
        if(n > 1) ret.eb(n, 1);
        return ret;
    }

    bool is_prime(const T &n) const{
        if(n == 1) return false;
        for(T i = 2; i*i <= n; i++){
            if(n%i == 0) return false;
        }
        return true;
    }

    vector<bool> Eratosthenes(const int &n) const{
        vector<bool> ret(n+1, true);
        if(n >= 0) ret[0] = false;
        if(n >= 1) ret[1] = false;
        for(int i = 2; i*i <= n; i++){
            if(!ret[i]) continue;
            for(int j = 2; i*j <= n; j++) ret[i*j] = false;
        }
        return ret;
    }
};

int main(){
    int T;
    cin >> T;
    Prime<int> P;
    Modulo<ll> M;
    while(T--){
        int N;
        cin >> N;
        if(N == 1) {cout << 1 << endl; continue;}
        int m = 2*N-1;
        int n = M.Euler_Totient(m);
        vector<int> ds = P.divisors(n);
        int ans = inf;
        for(auto &e: ds){
            if(M.pow(2, e, m) == 1) chmin(ans, e);
        }
        cout << ans << endl;
    }
}