#include <iostream>
#include <algorithm>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <numeric>
#include <bitset>
#include <cmath>

static const int MOD = 1000000007;
using ll = long long;
using u32 = unsigned;
using u64 = unsigned long long;
using namespace std;

template<class T> constexpr T INF = ::numeric_limits<T>::max()/32*15+208;

template<class T>
vector<T> divisor(T n){
    vector<T> ret;
    for(T i = 1; i * i <= n; i++) {
        if(n % i == 0) {
            ret.push_back(i);
            if(i * i != n) ret.push_back(n / i);
        }
    }
    sort(begin(ret), end(ret));
    return(ret);
}

int euler(int n){
    if(!n) return 0;
    int ans = n;
    for (int i = 2; i*i <= n; ++i) {
        if(n%i == 0){
            ans -= ans/i;
            while(n%i == 0) n /= i;
        }
    }
    if(n > 1) ans -= ans/n;
    return ans;
}

template <class T>
T pow_ (T x, T n, T M){
    uint64_t u = 1, xx = x;
    while (n > 0){
        if (n&1) u = u * xx % M;
        xx = xx * xx % M;
        n >>= 1;
    }
    return static_cast<T>(u);
};

int solve(int n){
    if(n == 1) return 1;
    for(auto &&d : divisor(euler(2*n-1))){
        if(pow_(2, d, 2*n-1) == 1) return d;
    }
    return -1;
}

int main() {
    int t;
    cin >> t;
    while(t--){
        int n;
        cin >> n;
        cout << solve(n) << "\n";
    }
    return 0;
}