#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#define _GLIBCXX_DEBUG
using namespace std;
using std::cout;
using std::cin;
using std::endl;
using ll=long long;
using ld=long double;
ll ILL=1167167167167167167;
const int INF=2100000000;
const ll mod=1e9+7;
#define rep(i,a) for (ll i=0;i<a;i++)
template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
template<class T> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> ll UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;}
template<class T> bool chmax(T &a,const T &b){if(a<b){a=b;return 1;}else return 0;}
template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
void yneos(bool a){if(a) cout<<"YES\n"; else cout<<"NO\n";}

//最大公約数
long long Gcd(long long a,long long b){
	if(b==0) return a;
	else return Gcd(b,a%b);
}

//最小公倍数
long long Lcm(long long a,long long b){
	return (a/Gcd(a,b))*b;
}
//カーマイケル数の出力
long long carmichael(long long a){
	long long ans=1,A=1;
	//2を素因数に持つときだけ場合わけ
	while(a%2==0) A*=2,a/=2;
	if(A==4) ans=2;
	else if(A>4) ans=A/4;
	A=a;
	for(long long k=3;k*k<=a;k++){
	//for(auto k:div){ //配列divをsqrt(a)以下の素数を全列挙するやつにする
		if(A%k==0){
			long long B=k-1;
			A/=k;
			while(A%k==0) A/=k,B*=k;
			ans=Lcm(ans,B);
		}
	}
	if(A!=1) ans=Lcm(ans,A-1);
	return ans;
}


//Nの正の約数を列挙する
vector<long long> Divisors(long long N){
    vector<long long> p,q;
    long long i=1,K=0;
    while(i*i<N){
        if(N%i==0){
            p.push_back(i);
            q.push_back(N/i);
            K++;
        }
        i++;
    }
    if(i*i==N) p.push_back(i);
    for(int i=K-1;i>=0;i--){
        p.push_back(q[i]);
    }
    return p;
}

ll jyo(ll x,ll y,ll z){
  ll H=y; //ここから
       ll a=1,b=x%z,c=1;
       while(H>0){
         a*=2;
         if(H%a!=0){
           H-=a/2;
           c*=b;
           c%=z;
         }
        b*=b;
         b%=z;
      } //ここまで
 return c;
}


void solve();
// oddloop
int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	
	int t=1;
	cin>>t;
	rep(i,t) solve();
}

void solve(){
	ll N;
	cin>>N;
	if(N==1){
		cout<<"1\n";
		return ;
	}
	ll C=carmichael(2*N-1);
	auto p=Divisors(C);
	for(auto x:p){
		if(jyo(2,x,2*N-1)==1){
			cout<<x<<"\n";
			return;
		}
	}
	cout<<"-1\n";
}