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.util.Scanner;
import java.awt.image.BandedSampleModel;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;
public class C{


    public static int[] primeFactors(int n,int count,int evenc)
    {
        // Print the number of 2s that divide n
        while (n%2==0)
        {
            evenc++;
            //System.out.print(2 + " ");
            n /= 2;
        }

        // n must be odd at this point.  So we can
        // skip one element (Note i = i +2)
        for (int i = 3; i <= Math.sqrt(n); i+= 2)
        {
            // While i divides n, print i and divide n
            while (n%i == 0)
            {
                count++;
                n /= i;
            }
        }

        // This condition is to handle the case whien
        // n is a prime number greater than 2
        if (n > 2)
            count++;
        return new int[]{evenc,count};
    }

    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        int cases = sc.nextInt();
        for(int i=0;i<cases;i++)
        {
            int n = sc.nextInt();
            if(n==1)
            {
                System.out.println("FastestFinger");
            }
            else if(n==2)
                {
                    System.out.println("Ashishgup");
                }
                else
            if(n%2==1)
            {
                System.out.println("Ashishgup");
            }
            else {

                int count=0;
                int evenc=0;
                int arr[] =primeFactors(n,count,evenc);
                count=arr[1];
                evenc=arr[0];

                if(count==0)
                {
                    System.out.println("FastestFinger");
                }
                else
                if(count==1&&evenc==1)
                {
                    System.out.println("FastestFinger");
                }
                else if(count>=1)
                {
                    System.out.println("Ashishgup");
                }
            }
        }

    }
}
