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.
import java.lang.*;
import java.io.*;
import java.util.*;

public class Rextester{
    static boolean isPrime(int n){
        for(int i=2;i*i<=n;i++){
            if(n%i==0){
                return false;
            }
        }
        return true;
    }
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        StringBuffer sb = new StringBuffer();
        while(t-->0){
            int n = Integer.parseInt(br.readLine());
            if(n==1){
                sb.append("FastestFinger\n");
            }
            else if(n==2){
                sb.append("Ashishgup\n");
            }
            else if((n&1)==1){
                sb.append("Ashishgup\n");
            }
            else{
                int z = 1;
                while(n%2==0){
                    n/=2;
                    z*=2;
                }
                if(n==1){
                    sb.append("FastestFinger\n");
                }
                else if(z>2){
                    sb.append("Ashishgup\n");
                }
                else{
                    if(isPrime(n)){
                        sb.append("FastestFinger\n");
                    }
                    else{
                        sb.append("Ashishgup\n");
                    }
                }
            }
        }
        br.close();
        System.out.println(sb);
    }
}