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;
bool comp(pair<long long, long long> a, pair<long long, long long> b) {
  if (a.first != b.first)
    return a.first < b.first;
  else
    return a.second > b.second;
}
long long ex(long long n, long long ans) {
  if (n == 1)
    return ans;
  else if (n % 2)
    return (ans % ((1000000007)) * ex(n / 2, (ans * ans) % (1000000007))) %
           (1000000007);
  else
    return ex(n / 2, (ans * ans) % (1000000007));
}
long long kmp(string x, long long m) {
  vector<long long> pi(m, 0);
  pi[0] = 0;
  long long j = 0;
  for (long long i = 1; i < m; i++) {
    j = pi[i - 1];
    while (j > 0 && x[i] != x[j]) j = pi[j - 1];
    if (x[j] == x[i]) j++;
    pi[i] = j;
  }
  return j;
}
string kmp1(string x, long long m) {
  vector<long long> pi(m, 0);
  pi[0] = 0;
  long long ma = 0;
  long long j = 0;
  long long pos = 0;
  for (long long i = 1; i < m; i++) {
    j = pi[i - 1];
    while (j > 0 && x[i] != x[j]) j = pi[j - 1];
    if (x[j] == x[i]) j++;
    pi[i] = j;
    if (x[i] == '#') pos = i;
  }
  long long p = pos;
  for (long long i = (pos); i < (m); ++i) {
    if (pi[i] > ma) {
      ma = pi[i];
      p = i;
    }
  }
  return x.substr(p - ma + 1, ma);
}
void dfs(vector<long long> adj[], long long fl[], long long i, long long& cn) {
  fl[i] = 1;
  cn++;
  for (long long j = (0); j < (adj[i].size()); ++j) {
    if (!fl[adj[i][j]]) {
      dfs(adj, fl, adj[i][j], cn);
    }
  }
}
int isp(long long x) {
  for (long long i = 2; i * i <= x; i++)
    if (x % i == 0) return 0;
  return 1;
}
struct Compare {
  bool operator()(long long const& p1, long long const& p2) {
    if (p1 < p2) {
      return true;
    }
    return false;
  }
};
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t1 = 1;
  cin >> t1;
  while (t1--) {
    long long n;
    cin >> n;
    if ((n % 2 && n > 1) || n == 2)
      cout << ("Ashishgup") << " ";
    else if (!(n & (n - 1)) || n == 1)
      cout << ("FastestFinger") << " ";
    else {
      if (n % 4 == 0)
        cout << ("Ashishgup") << " ";
      else {
        n = n / 2;
        if (isp(n))
          cout << ("FastestFinger") << " ";
        else
          cout << ("Ashishgup") << " ";
      }
    }
    cout << "\n";
    ;
  }
}
