//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
#define rep(i, n) for(int i=0; i<n; ++i)
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
using namespace std;
using ll = int64_t;
using ld = long double;
using P = pair<int, int>;
using vs = vector<string>;
using vi = vector<int>;
using vvi = vector<vi>;
template<class T> using PQ = priority_queue<T>;
template<class T> using PQG = priority_queue<T, vector<T>, greater<T> >;
const int INF = 0xccccccc;
const ll LINF = 0xcccccccccccccccLL;
template<typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {return a < b && (a = b, true);}
template<typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {return a > b && (a = b, true);}
template<typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) { return is >> p.first >> p.second;}
template<typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) { return os << p.first << ' ' << p.second;}

struct Sieve {
	int n;
	vector<int> f, primes;
	Sieve(int n=1):n(n), f(n+1) {
		f[0] = f[1] = -1;
		for(int i=2; i<=n; ++i) {
			if(!f[i]) {
				primes.emplace_back(i);
				f[i] = i;
			}
			for(int p:primes) {
				int u = p*i;
				if(u > n or p > f[i]) break;
				f[u] = p;
			}
		}
	}
	//素数判定
	bool isPrime(int x) {return f[x] == x;}
	//素数判定(1つ用)(宣言はsqrt(x)のサイズで)
	bool isPrime1(int64_t x) {
		bool m = true;
		for(int z:primes) {
			if(!(x%z)) {
				m = false;
				break;
			}
		}
		return m;
	}
	//素数列挙
	vector<int > factorList(int x) {
		assert(x <= n);
		vector<int> res;
		while(x != 1) {
			res.emplace_back(f[x]);
			x /= f[x];
		}
		return res;
	}
	//素因数分解　pair(素数, 素因数の数)
	vector<pair<int, int> > factor(int x) {
		vector<int> fl = factorList(x);
		if(fl.size() == 0) return {};
		vector<pair<int, int> > res(1, pair<int, int>(fl[0], 0));
		for(int p : fl) {
			if(res.back().first == p) {
				++res.back().second;
			} else {
				res.emplace_back(p, 1);
			}
		}
		return res;
	}
	//素数列挙(1つ用)(宣言はsqrt(x)のサイズで)
	vector<int64_t> factorList1(int64_t x) {
		vector<int64_t> vec;
		for(int z:primes) {
			while(!(x%z)) {
				vec.emplace_back(z);
				x /= z;
			}
		}
		if(x != 1) vec.emplace_back(x);
		return vec;
	}
	//素数列挙(1つ用)(宣言はsqrt(x)のサイズで)　pair(素数, 素因数の数)
	vector<pair<int64_t, int> > factor1(int64_t x) {
		vector<int64_t> vec = factorList1(x);
		vector<pair<int64_t, int> > vecc;
		for(vector<int64_t>::iterator itr = vec.begin(); itr != vec.end(); ++itr) {
			if(itr != vec.begin() && *itr == *(itr-1)) {
				(vecc.end()-1)->second++;
			} else {
				vecc.emplace_back(pair<int64_t, int>(*itr, 1));
			}
		}
		return vecc;
	}
	//約数列挙
	vector<int64_t> div1(int64_t x) {
		vector<int64_t> res(1, 1);
		vector<pair<int64_t, int> > fac = factor1(x);
		for(int i = 0; i < int(fac.size()); ++i) {
			int si = res.size();
			for(int j = 0; j < fac[i].second; ++j) {
				for(int k = 0; k < si; ++k) {
					res.emplace_back(res[k+j*si]*fac[i].first);
				}
			}
		}
		sort(res.begin(), res.end());
		return res;
	}
} pp(100000);

struct barrett {
	unsigned int _m;
	uint64_t im;
	barrett(unsigned int m):_m(m), im(uint64_t(-1)/m + 1) {}
	unsigned int umod() const {return _m;}
	unsigned int mul(unsigned int a, unsigned int b) const {
		uint64_t z = a;
		z *= b;
		uint64_t x = uint64_t(((unsigned __int128)(z)*im) >> 64);
		unsigned int v = (unsigned int)(z-x*_m);
		if(_m <= v) v += _m;
		return v;
	}
};

constexpr int64_t safe_mod(int64_t x, int64_t m) {
	x %= m;
	if(x < 0) x += m;
	return x;
}

constexpr pair<int64_t, int64_t> inv_gcd(int64_t a, int64_t b) {
	a = safe_mod(a, b);
	if(a == 0) return {b, 0};
	int64_t s = b, t = a;
	int64_t m0 = 0, m1 = 1;
	while(t) {
		int64_t u = s/t;
		s -= t*u;
		m0 -= m1*u;
		int64_t tmp = s;
		s = t;
		t = tmp;
		tmp = m0;
		m0 = m1;
		m1 = tmp;
	}
	if(m0 < 0) m0 += b/s;
	return {s, m0};
}

int64_t pow_mod(int64_t x, int64_t n, int m) {
	if(m == 1) return 0;
	barrett bt((unsigned int)(m));
	unsigned int r = 1, y = (unsigned int)(safe_mod(x, m));
	while(n) {
		if(n&1) r = bt.mul(r, y);
		y = bt.mul(y, y);
		n >>= 1;
	}
	return r;
}

int64_t inv_mod(int64_t x, int64_t m) {
	pair<int64_t, int64_t> z = inv_gcd(x, m);
	assert(z.first == 1);
	return z.second;
}

//(y, z) answer mod z = y, 無理な時は(-1, -1)
pair<int64_t, int64_t> crt(const vector<int64_t> &r, const vector<int64_t> &m) {
	int n = int(r.size());
	int64_t r0 = 0, m0 = 1;
	for(int i = 0; i < n; i++) {
		assert(1 <= m[i]);
		int64_t r1 = safe_mod(r[i], m[i]), m1 = m[i];
		if(m0 < m1) {
			swap(r0, r1);
			swap(m0, m1);
		}
		if(m0 % m1 == 0) {
			if(r0 % m1 != r1) return {-1, -1};
			continue;
		}
		int64_t g, im;
		tie(g, im) = inv_gcd(m0, m1);
		int64_t u1 = (m1/g);
		if((r1-r0)%g) return {-1, -1};
		int64_t x = (r1-r0)/g%u1 * im % u1;
		r0 += x*m0;
		m0 *= u1;
		if(r0 < 0) r0 += m0;
	}
	return {r0, m0};
}

//[0, n) (a*i+b)/m
int64_t floor_sum(int64_t n, int64_t m, int64_t a, int64_t b) {
	int64_t ans = 0;
	if(a >= m) {
		ans += ((n-1)*n>>1)*(a/m);
		a %= m;
	}
	if(b >= m) {
		ans += n*(b/m);
		b %= m;
	}
	int64_t y_max = (a*n+b)/m, x_max = y_max*m-b;
	if(y_max == 0) return ans;
	ans += (n - (x_max+a-1)/a) * y_max;
	ans += floor_sum(y_max, a, m, (a - x_max%a)%a);
	return ans;
}

//head



int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	int t;
	cin >> t;
	while(t--) {
		int n;
		cin >> n;
		if(n == 1) {
			cout << "1\n";
			continue;
		}
		int mod = n*2-1;
		auto z = pp.factor1(mod);
		int u = mod;
		for(P x:z) {
			u /= x.first;
			u *= x.first-1;
		}
		auto zz = pp.div1(u);
		for(auto x:zz) {
			if(pow_mod(2, x, mod) == 1) {
				cout << x << '\n';
				break;
			}
		}
	}
}