#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1e9 + 7;
const long long MAXN = 2e6 + 1;
string first() { return "Ashishgup"; }
string second() { return "FastestFinger"; }
void solve() {
  long long n;
  cin >> n;
  long long cnt1 = 0, cnt2 = 0;
  if (n == 1) {
    cout << second() << '\n';
    return;
  }
  if (n == 2) {
    cout << first() << '\n';
    return;
  }
  for (long long i = 2; i * i <= n; ++i) {
    while (n % i == 0) {
      n /= i;
      if (i & 1) {
        cnt1++;
      } else if (i == 2) {
        cnt2++;
      }
    }
  }
  if (n != 1) {
    if (n & 1) {
      cnt1++;
    } else if (n == 2) {
      cnt2++;
    }
  }
  if (cnt2 == 0) {
    cout << first() << '\n';
    return;
  }
  if (cnt2 == 1) {
    cout << (cnt1 == 1 ? second() : first()) << '\n';
    return;
  }
  cout << (cnt1 == 0 ? second() : first()) << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr), cout.tie(nullptr);
  int test = 1;
  cin >> test;
  for (int i = 1; i <= test; ++i) {
    solve();
  }
  return 0;
}

### Prompt

Your challenge is to write a cpp solution to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1e9 + 7;
const long long MAXN = 2e6 + 1;
string first() { return "Ashishgup"; }
string second() { return "FastestFinger"; }
void solve() {
  long long n;
  cin >> n;
  long long cnt1 = 0, cnt2 = 0;
  if (n == 1) {
    cout << second() << '\n';
    return;
  }
  if (n == 2) {
    cout << first() << '\n';
    return;
  }
  for (long long i = 2; i * i <= n; ++i) {
    while (n % i == 0) {
      n /= i;
      if (i & 1) {
        cnt1++;
      } else if (i == 2) {
        cnt2++;
      }
    }
  }
  if (n != 1) {
    if (n & 1) {
      cnt1++;
    } else if (n == 2) {
      cnt2++;
    }
  }
  if (cnt2 == 0) {
    cout << first() << '\n';
    return;
  }
  if (cnt2 == 1) {
    cout << (cnt1 == 1 ? second() : first()) << '\n';
    return;
  }
  cout << (cnt1 == 0 ? second() : first()) << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr), cout.tie(nullptr);
  int test = 1;
  cin >> test;
  for (int i = 1; i <= test; ++i) {
    solve();
  }
  return 0;
}

```