Ashishgup and FastestFinger play a game. 

They start with a number n and play in turns. In each turn, a player can make any one of the following moves:

  * Divide n by any of its odd divisors greater than 1. 
  * Subtract 1 from n if n is greater than 1. 



Divisors of a number include the number itself.

The player who is unable to make a move loses the game.

Ashishgup moves first. Determine the winner of the game if both of them play optimally.

Input

The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.

The only line of each test case contains a single integer — n (1 ≤ n ≤ 10^9).

Output

For each test case, print "Ashishgup" if he wins, and "FastestFinger" otherwise (without quotes).

Example

Input


7
1
2
3
4
5
6
12


Output


FastestFinger
Ashishgup
Ashishgup
FastestFinger
Ashishgup
FastestFinger
Ashishgup

Note

In the first test case, n = 1, Ashishgup cannot make a move. He loses.

In the second test case, n = 2, Ashishgup subtracts 1 on the first move. Now n = 1, FastestFinger cannot make a move, so he loses.

In the third test case, n = 3, Ashishgup divides by 3 on the first move. Now n = 1, FastestFinger cannot make a move, so he loses.

In the last test case, n = 12, Ashishgup divides it by 3. Now n = 4, FastestFinger is forced to subtract 1, and Ashishgup gets 3, so he wins by dividing it by 3.
#include <bits/stdc++.h>
using namespace std;
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  cout << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cout.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
void fastIO() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
long long modexpo(long long a, long long b) {
  if (a == 0) return 0;
  if (a == 1 or b == 0) return 1;
  if (b == 1) return a;
  if (b & 1)
    return (a % 1000000007 * modexpo(a, b - 1) % 1000000007) % 1000000007;
  return modexpo(a % 1000000007 * a % 1000000007, b / 2) % 1000000007;
}
void printv(vector<long long> v) {
  for (auto& x : v) {
    cout << x << " ";
  }
  cout << "\n";
}
string to_string1(long long x) {
  stringstream ss;
  ss << x;
  return ss.str();
}
long long to_integer(string s) {
  stringstream ss(s);
  long long x;
  ss >> x;
  return x;
}
long long a, b, c, d;
void input() { cin >> a >> b >> c >> d; }
long double pi = 3.1415926535;
void printYes() { cout << "Ashishgup\n"; }
void printNo() { cout << "FastestFinger\n"; }
long long t, n, p;
long long spf[8000 + 1];
void fill_spf() {
  memset(spf, 0, sizeof spf);
  for (long long i = 2; i <= 8000; i++) {
    if (spf[i] == 0) {
      for (long long j = i; j <= 8000; j++) {
        if (spf[j] == 0) {
          spf[j] = i;
        }
      }
    }
  }
}
bool solve(long long n) {
  n = n / 2;
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 or n % 3 == 0) return false;
  for (long long i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 or n % (i + 2) == 0) return false;
  return true;
}
int main() {
  fastIO();
  fill_spf();
  cin >> t;
  while (t--) {
    cin >> n;
    if (n == 1) {
      printNo();
      continue;
    }
    if (n == 2) {
      printYes();
      continue;
    }
    long long x = n;
    long long two = 0;
    while (x % 2 == 0) {
      two++;
      x = x / 2;
    }
    if (x == 1) {
      printNo();
      continue;
    }
    if (two == 0 or two > 1) {
      printYes();
      continue;
    }
    if (not solve(n)) {
      printYes();
      continue;
    } else {
      printNo();
      continue;
    }
  }
  return 0;
}
