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.BufferedWriter;
import java.io.IOException;
import java.util.StringTokenizer;
import java.io.OutputStreamWriter;
import java.io.InputStreamReader;
import java.io.FileOutputStream;
public class NumberGame{
	public static void main(String[] args)throws IOException{
		FastReader sc = new FastReader();
		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(java.io.FileDescriptor.out),"ASCII"),512);
		int t = sc.nextInt();
		while(t-- > 0){
			int n = sc.nextInt();
			if(n==1) out.write("FastestFinger");
			else if(n==2) out.write("Ashishgup");
			else if(n%2==1) out.write("Ashishgup");
			else{
				int counte = 0;
				int counto = 0;
				for(int i=2;i<=Math.sqrt(n);i++){
					if((n%i) == 0){
						while((n%i)==0){
							n /= i;
							if(i==2) counte++;
							else counto++;
						}
					}
				}
				if(n==2) counte++;
				else if(n>2) counto++;
				if(counto == 0) out.write("FastestFinger");
				else{
					if(counte == 1){
						if(counto == 1){
							out.write("FastestFinger");
						}else{
							out.write("Ashishgup");
						}
					}else{
						out.write("Ashishgup");
					}
				}
			}
			out.write('\n');
			out.flush();
		}
	}
}
class FastReader{
	BufferedReader br;
	StringTokenizer st;
	public FastReader(){
		br = new BufferedReader(new InputStreamReader(System.in));
	}
	String next(){ 
		while (st == null || !st.hasMoreElements()){ 
			try{ 
				st = new StringTokenizer(br.readLine()); 
			} 
			catch (IOException  e){ 
				e.printStackTrace(); 
			} 
		} 
		return st.nextToken(); 
	}
	int nextInt(){ 
        return Integer.parseInt(next()); 
	}
    long nextLong(){ 
        return Long.parseLong(next()); 
    }
    double nextDouble(){ 
        return Double.parseDouble(next()); 
    }
    String nextLine(){ 
        String str = ""; 
        try{ 
            str = br.readLine(); 
        } 
		catch (IOException e){ 
            e.printStackTrace(); 
        } 
        return str; 
    }
}