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.*;
import java.util.*;


public class C_H1 {
		
	static Scanner sc;
	static PrintWriter out;
	
	public static void main(String[] args) throws Exception{
	sc  = new Scanner(System.in);
	out = new PrintWriter(System.out);
	
		int TC  =sc.nextInt();
		
		while(TC-->0)
		{
			int n =sc.nextInt();
			
			if(n==1)
			{
				out.println("FastestFinger");
				continue;
			}
			if(n==2)
			{
				out.println("Ashishgup");
				continue;
			}
			if(n%2==1)
			{
				out.println("Ashishgup");
				continue;
			}
			int twos = 0;
			while(n%2==0)
			{
				n = n/2;
				twos++;
			}
			
			if(n==1)
			{
				out.println("FastestFinger");
				continue;
			}
			
			if(twos == 1)
			{
				if(isOddPrime(n))
				{
					out.println("FastestFinger");
				}
				else
				{
					out.println("Ashishgup");
				}
			}
			else
			{
				out.println("Ashishgup");
			}
		}
		out.flush();
		out.close();
	}
	
	
	static boolean isOddPrime(int x) {
		int limit = (int)(Math.sqrt(x)) + 1;
		for(int i=3;i<=limit;i++)
		{
			if(x%i==0)
				return false;
		}
		return true;
	}
	static class Scanner{
		StringTokenizer st;
		BufferedReader br;
		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
		public Scanner(FileReader file) {
			br = new BufferedReader(file);
		}
		public String next() throws IOException {
			while(st == null || !st.hasMoreTokens())
			{
				st = new StringTokenizer(br.readLine());
			}
			return st.nextToken();
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
		public int nextInt()throws IOException{
			return Integer.parseInt(next());
		}
		public double nextDouble()throws IOException{
			return Double.parseDouble(next());
		}
		public char nextChar()throws IOException{
			return next().charAt(0);
		}
		public long nextLong()throws IOException{
			return Long.parseLong(next());
		}
		public boolean ready() throws IOException {
			return br.ready();
		}
		public void waitForInput() throws InterruptedException {
			Thread.sleep(5000);
		}
	}


}
