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;
vector<bool> vis;
vector<vector<int> > adj;
void initialize() {
  for (int i = 0; i < 100000; i++) vis[i] = false;
}
bool bfs(int s, int u) {
  queue<int> q;
  initialize();
  q.push(s);
  while (!q.empty()) {
    int s = q.front();
    if (s == u) return true;
    q.pop();
    vis[s] = true;
    for (int i = 0; i < adj[s].size(); i++) {
      if (vis[adj[s][i]] == false) {
        vis[adj[s][i]] = true;
        q.push(adj[s][i]);
      }
    }
  }
  return false;
  initialize();
}
void dfs(int s) {
  if (vis[s]) return;
  vis[s] = true;
  for (int i = 0; i < adj[s].size(); i++) {
    if (!vis[adj[s][i]]) dfs(adj[s][i]);
  }
}
long long expo(long long x, long long n, long long p) {
  if (n == 0) return 1 % p;
  long long ans = 1, base = x;
  while (n > 0) {
    if (n % 2 == 1) {
      ans = (ans * base) % p;
      n--;
    } else {
      base = (base * base) % p;
      n /= 2;
    }
  }
  if (ans < 0) ans = (ans + p) % p;
  return ans;
}
long long power(long long x, long long y) {
  long long k = 1;
  while (y--) {
    k = k * x;
  }
  return k;
}
void addedge(int x, int y) {
  adj[x].push_back(y);
  adj[y].push_back(x);
}
bool check_prime(long long n) {
  long long N = 50000;
  for (long long i = 2; i < min(N, n); i++)
    if (n % i == 0) return 0;
  return 1;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long t, n, lose;
  cin >> t;
  while (t--) {
    cin >> n;
    lose = 0;
    if (n == 1)
      lose = 1;
    else if (n > 2 && n % 2 == 0) {
      if ((n & (n - 1)) == 0)
        lose = 1;
      else if (n % 4 != 0 && check_prime(n / 2))
        lose = 1;
    }
    if (lose)
      cout << "FastestFinger" << '\n';
    else
      cout << "Ashishgup" << '\n';
  }
}
