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;
const long long INF = LLONG_MAX;
const long long SZ = 1e6 + 5;
const long long mod = 1e9 + 7;
long long n;
bool st[SZ];
vector<long long> prime;
void sieve() {
  long long i, j;
  st[0] = st[1] = 1;
  for (i = 2; i * i < SZ; i++) {
    if (!st[i]) {
      for (j = i * i; j < SZ; j += i) st[j] = 1;
    }
  }
  prime.push_back(2);
  for (i = 3; i < SZ; i += 2) {
    if (!st[i]) prime.push_back(i);
  }
}
bool check_prime(long long x) {
  for (long long i = 1; i < prime.size() && prime[i] * prime[i] <= x; i++) {
    if (x % prime[i] == 0) return 1;
  }
  return 0;
}
map<long long, bool> is_pow;
void cal_pw2() {
  long long i, x = 1, y;
  for (i = 0; i < 35; i++) {
    y = x;
    is_pow[y] = 1;
    x *= 2;
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  sieve();
  cal_pw2();
  long long cs = 0, tc = 1, x, y, z, i, j, k, g, p, q, ans = 0, sum = 0, c = 0,
            t = 0;
  string s, s1, s2;
  cin >> tc;
  while (tc--) {
    cin >> n;
    if (n == 1) {
      cout << "FastestFinger\n";
      continue;
    }
    if (n == 2 || n % 2) {
      cout << "Ashishgup\n";
      continue;
    }
    if (is_pow[n]) {
      cout << "FastestFinger\n";
      continue;
    }
    c = 0;
    while (n % 2 == 0) {
      n /= 2;
      c++;
    }
    bool f = check_prime(n);
    if (c == 1) {
      if (!f)
        cout << "FastestFinger\n";
      else
        cout << "Ashishgup\n";
    } else
      cout << "Ashishgup\n";
  }
  return 0;
}
