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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    static void div(int n, ArrayList<Integer> list) 
    { 
        for (int i=1; i<=Math.sqrt(n); i++) 
        { 
            if (n%i==0) 
            { 
                if (n/i == i) {
                    if(i%2!=0 && i!=1) list.add(i);
                } 
                else {
                    if(i%2!=0 && i!=1) list.add(i);
                    int val=n/i;
                    if(val%2!=0 && val!=1) list.add(val);
                }
            } 
        } 
    } 
	public static void main(String[] args) {
		FastScanner sc=new FastScanner();
		PrintWriter out=new PrintWriter(System.out);
		
		int test = sc.nextInt();
		while(test-->0)
		{
		    int n = sc.nextInt();
    // 		int []arr = new int[2*n];
    // 		for(int i=0;i<2*n;i++)
    // 		   arr[i] = sc.nextInt();
    		if(n==1)
    		    System.out.println("FastestFinger");
    		else if(n%2!=0 || n==2){
    		    System.out.println("Ashishgup");
    		}   
    		else{
    		    ArrayList<Integer> list = new ArrayList<>();
    		    boolean isA=true;
    		    while(true){
    		        div(n, list);
    		        Collections.sort(list);
    		        if(list.size()==0 || (list.size()==1 && (n/list.get(0)==2))){
    		            if(isA)
    		                System.out.println("FastestFinger");
    		            else
    		                System.out.println("Ashishgup");
    		            break;
    		        }
    		        int len = list.size();
    		        if(n/list.get(len-1) == 2)
    		           n=n/list.get(len-2);
    		        else
    		           n=n/list.get(len-1);
    		           
                    isA=!isA;   
                    list.clear();
    		    }
    		}
    	   
		}
		    
		out.close();
	}
	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;
 
		public FastScanner() {
			try	{
				br = new BufferedReader(new InputStreamReader(System.in));
				st = new StringTokenizer(br.readLine());
			} catch (Exception e){e.printStackTrace();}
		}
 
		public String next() {
			if (st.hasMoreTokens())	return st.nextToken();
			try {st = new StringTokenizer(br.readLine());}
			catch (Exception e) {e.printStackTrace();}
			return st.nextToken();
		}
 
		public int nextInt() {return Integer.parseInt(next());}
 
		public long nextLong() {return Long.parseLong(next());}
 
		public double nextDouble() {return Double.parseDouble(next());}
 
		public String nextLine() {
			String line = "";
			if(st.hasMoreTokens()) line = st.nextToken();
			else try {return br.readLine();}catch(IOException e){e.printStackTrace();}
			while(st.hasMoreTokens()) line += " "+st.nextToken();
			return line;
		}
	}
}




















