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#include <bits/stdc++.h>

using namespace std;

#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return {i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifdef LOCAL
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
  ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
  *this << "[";
  for (c it = d.b; it != d.e; ++it)
    *this << ", " + 2 * (it == d.b) << *it;
  ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
};
#define imie(x...) " [" #x ": " << (x) << "] "

using ll = long long;

namespace Rho {
vector<ll> Rozklad(ll n);

vector<ll> witness = {2, 325, 9375, 28178, 450775, 9780504, 1795265022}; ll mul(ll a, ll b, ll mod) { return (__int128) a * b % mod; } ll my_pow(ll a, ll b, ll mod) { ll res = 1; while(b) { if(b % 2) res = mul(res, a, mod); a = mul(a, a, mod); b /= 2; } return res; } bool test(ll n) { if(n == 2) return true; if(n < 2 || n % 2 == 0) return false; ll d = n - 1, s = 0; while(d % 2 == 0) { d /= 2; ++s; } for(auto i : witness) if(i % n) { ll x = my_pow(i, d, n); if(x == 1) continue; bool zlozona = true; for(int j = 0; j < s; ++j) { if(x == n - 1) { zlozona = false; break; } x = mul(x, x, n); } if(zlozona) return false; } return true; } ll f(ll x, ll mod, ll c) { ll y = mul(x, x, mod) + c; if(y > mod) y -= mod; return y; } void rho(ll n, vector<ll> & w) { if(n <= 1) return; if(test(n)) { w.push_back(n); return; } for(ll c = 1; true; ++c) { ll x = 2, y = 2, d = 1; while(d == 1) { x = f(x, n, c); y = f( f(y,n,c), n, c); d = __gcd(abs(x - y), n); } if(d < n) { rho(d, w); rho(n / d, w); return; } } } vector<ll> Rozklad(ll n) { vector<ll> w; for(int i = 2; i <= 100; ++i) while(n % i == 0) { n /= i; w.push_back(i); } rho(n, w); sort(w.begin(), w.end()); return w; }
}  // namespace Rho

template <typename T> T Maxi(T& a, T b) { return a = max(a, b); }
template <typename T> T Mini(T& a, T b) { return a = min(a, b); }

#include "dzilib.h"
/*
int GetT();
long long GetN();
int GetQ();
long long GetC();
long long Ask(long long y);
void Answer(long long z);
*/

ll Dzielniki(ll n) {
  ll last_p = -1;
  ll last_a = 0;
  ll wynik = 1;
  for (const ll p : Rho::Rozklad(n)) {
    if (p == last_p) {
      last_a++;
    } else {
      if (last_p != -1) {
        wynik *= (last_a + 1);
      }
      last_p = p;
      last_a = 1;
    }
  }
  if (last_p != -1) {
    wynik *= (last_a + 1);
  }
  return wynik;
}

std::mt19937 rnd(0x8923921);

struct Test {
  ll Run(ll n) {
    const ll y236 = Znajdz236(uniform_int_distribution<ll>(1, n)(rnd));
    assert(y236 != -1);
    debug() << imie(y236);

    vector<ll> kandydaci;
    for (ll i = (y236 >> 36) + 1; (i << 36) <= n + y236; i++) {
      const ll kandydat = (i << 36) - y236;
      assert(kandydat >= 1);
      if (OkKandydat(kandydat)) {
        kandydaci.push_back(kandydat);
      }
    }
    assert(!kandydaci.empty());

    while ((int) kandydaci.size() > 1) {
      debug() << imie(kandydaci.size()) imie(zapytania.size());
      std::uniform_int_distribution<ll> dist(0, GetC());
      const ll y = dist(rnd);
      const ll d = Zapytanie(y);
      for (int i = 0; i < (int) kandydaci.size(); i++) {
        if (Dzielniki(kandydaci[i] + y) != d) {
          swap(kandydaci[i], kandydaci.back());
          kandydaci.pop_back();
        }
      }
    }

    debug() << imie(kandydaci);
    assert((int) kandydaci.size() == 1);
    return kandydaci[0];
  }

  ll Znajdz236(ll start_y) {
    const ll y = Baktracz(0, start_y);
    if (y != -1) return y;
    return Baktracz(0, start_y + 1ll);
  }

  // 2^pot | (x + y) and 2^(pot+1) not| (x + y)
  // Returns y such that 2^36 | (x + y) or -1 if contradiction.
  ll Baktracz(int pot, ll y) {
    if (Zapytanie(y) % (pot + 1) != 0) {
      return -1;
    }
    if (pot >= 36) {
      return y;
    }

    ll y1 = y + (1ll << pot);
    ll y2 = y + (1ll << pot) + (1ll << (pot + 1));
    if (uniform_int_distribution<int>(0, 1)(rnd) == 1) {
      swap(y1, y2);
    }

    const ll res = Baktracz(pot + 1, y1);
    if (res != -1) return res;
    return Baktracz(pot + 1, y2);
  }

  ll Zapytanie(ll y) {
    auto it = zapytania.find(y);
    if (it != zapytania.end()) {
      return it->second;
    }
    return zapytania[y] = Ask(y);
  }

  bool OkKandydat(ll x) {
    for (const auto& [y, d] : zapytania) {
      if (Dzielniki(x + y) != d) {
        return false;
      }
    }
    return true;
  }

  unordered_map<ll, ll> zapytania;
};

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);

  rnd.seed(time(NULL));

  const int t = GetT();
  for (int i = 0; i < t; i++) {
    Answer(Test().Run(GetN()));
  }
  return 0;
}