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.
// package Round_651;

import java.io.*;
import java.util.*;

public class Problem_C {  
    public static void main(String[] args) {
        FastReader in = new FastReader();
        HashSet<Integer> primes = new HashSet<Integer>();
        boolean[] list = new boolean[(int) Math.ceil(Math.pow(10, 4.5)) + 2];
        Arrays.fill(list, true);
        
        for(int i = 2; i < list.length; i++) {
        	if(list[i] == true) {
        		for(int j = i * i; j < list.length; j += i) {
            		list[j] = false;
            	}
        	}
        }
        
        for(int i = 3; i < list.length; i++) {
        	if(list[i]) {
        		primes.add(i);
        	}
        }
        
        int numTrials = in.nextInt();
        while(numTrials --> 0) {
            int num = in.nextInt();
            
            if(num == 1) {
            	System.out.println("FastestFinger");
            }
            else if(num % 2 == 1 || num == 2) {
            	System.out.println("Ashishgup");
            }
            else {
            	int oddDivs = 0;
            	int div = 3;
            	
            	int num2s = 0;
            	while(num % 2 == 0) {
            		num /= 2;
            		num2s++;
            	}
            	
            	if(primes.contains(num)) {
            		oddDivs = 1;
            	}
            	else if(num != 1){
            		Iterator<Integer> iter = primes.iterator();
            		boolean found = false;
            		while(iter.hasNext()) {
            			int n = iter.next();           			
            			if(num % n == 0) {
            				found = true;
            				break;
            			}
            		}
            		
            		if(found) {
            			oddDivs = 2;
            		}
            		else {
            			oddDivs = 1;
            		}
            	}
            	
            	if(oddDivs == 0) {
            		System.out.println("FastestFinger");
            	}
            	else if(oddDivs == 1) {
            		if(num2s == 1) {
            			System.out.println("FastestFinger");
            		}
            		else {
            			System.out.println("Ashishgup");
            		}
            	}
            	else {
            		System.out.println("Ashishgup");
            	}
            }
        }
    }
    
    static 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; 
        } 
    } 
}
