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;
long long int modInverse(long long int a, long long int m) {
  long long int m0 = m;
  long long int y = 0, x = 1;
  if (m == 1) return 0;
  while (a > 1) {
    long long int q = a / m;
    long long int t = m;
    m = a % m, a = t;
    t = y;
    y = x - q * y;
    x = t;
  }
  if (x < 0) x += m0;
  return x;
}
long long int power(long long int x, long long int y, long long int p) {
  long long int res = 1;
  x = x % p;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
bool sortinrev(const pair<int, int>& a, const pair<int, int>& b) {
  if (a.first == b.first) return b.second > a.second;
  return a.first > b.first;
}
void run(vector<long long int> v) {
  for (int i = 0; i < v.size(); i++) cout << v[i] << " ";
  cout << endl;
}
void solve() {
  int n;
  cin >> n;
  string F = "FastestFinger", A = "Ashishgup";
  if (n == 1) {
    cout << F << endl;
    return;
  }
  if (n == 2) {
    cout << A << endl;
    return;
  } else if ((n & (n - 1)) == 0) {
    cout << F << endl;
    return;
  } else if (n & 1) {
    cout << A << endl;
    return;
  }
  int twos = 0, oth = 0;
  while (n % 2 == 0) {
    n = n / 2;
    twos++;
  }
  for (int i = 3; i * i <= n; i += 2) {
    int j = i;
    while (n % j == 0) {
      n = n / j;
      oth++;
    }
  }
  if (n > 2) oth++;
  if (twos == 1) {
    if (oth == 1) {
      cout << F << endl;
      return;
    } else {
      cout << A << endl;
    }
  } else {
    cout << A << endl;
    return;
  }
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}
