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.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Collections;
import java.util.*;

public class Main {
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int cases=Integer.valueOf(br.readLine());
		while(cases!=0)
		{
			cases--;
			int n=Integer.valueOf(br.readLine());
			if(n==1)
			{
				System.out.println("FastestFinger");
			}
			else if(n%2!=0)
			{
				System.out.println("Ashishgup");
			}
			else
			{
				if(n==2)
					System.out.println("Ashishgup");
				else if((n&(n-1))==0)
				{
					System.out.println("FastestFinger");
				}
				else
				{
					if(n%4==0)
					{
						System.out.println("Ashishgup");
					}
					else
					{
						n=n/2;
						int cnt=0;
						for(int i=3;i*i<=n;i=i+2)
						{
							while(n%i==0)
							{
								cnt++;
								n=n/i;
							}
						}
						if(n>2)
							cnt++;
						if(cnt>=2)
						{
							System.out.println("Ashishgup");
						}
						else
							System.out.println("FastestFinger");
					}
				}
			}
		}
		}}
