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.*;
import java.math.*;
 
public class Education_89_2
{
	InputReader in;PrintWriter pw;
	void solve(int test) throws Exception
	{
		int n = ni();
		if(n==1)
		{
			pn("FastestFinger");
		}
		else if(n==2)
		{
			pn("Ashishgup");
		}
		else if((n&1)==1)
		{
			pn("Ashishgup");
		}
		else if((n&1)==0)
		{
			int num=n;
			while(n%2==0)
			{
				n = n/2;
			}
			if(n==1)
			{
				pn("FastestFinger");
			}
			else if(num/n==2)
			{
				int count=0;
				for(int i=3;i<=Math.sqrt(n);i++)
				{
					while(n%i==0)
					{
						n=n/i;
						count++;
					}
				}
				if(n>1)
				{
					count++;
				}
				if(count>1)
				{
					pn("Ashishgup");
				}
				else
				{
					pn("FastestFinger");
				}
			}
			else if(num/n>2)
			{
				pn("Ashishgup");
			}
		}
	}
	void run() throws Exception 
	{
		in = new InputReader();
		pw = new PrintWriter(System.out);
		int test = ni();
		while(test--!=0){solve(test);}
		pw.close();
	}
	public static void main(String[] args) throws Exception
	{
		new Education_89_2().run();
	}
	void p(Object o){pw.print(o);}
	void pn(Object o){pw.println(o);}
	void pn(){pw.println();}
	void spn(Object o){System.out.println(o);};
	String nln() throws Exception {return in.nextLine();}
	int ni() throws Exception {return Integer.parseInt(in.next());}
	double nd() throws Exception {return Double.parseDouble(in.next());}
	long nl() throws Exception {return Long.parseLong(in.next());}
	class InputReader
	{
		BufferedReader br;
		StringTokenizer st;
 
		public InputReader()
		{
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		public InputReader(String s) throws IOException
		{
			br = new BufferedReader(new FileReader(s));
		}
 
		String next() throws Exception
		{
			if(st==null || !st.hasMoreElements())
			{
				try
				{
					st = new StringTokenizer(br.readLine());
				}
				catch(IOException e)
				{
					throw new Exception(e.toString());
				}
			}
			return st.nextToken();
		}
 
		String nextLine() throws Exception
		{
			String str = "";
			try
			{
				str = br.readLine();
			}
			catch(IOException e)
			{
				throw new Exception(e.toString());
			}
			return str;
		}
	}
}
