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.util.*;
import java.io.*;
import java.math.*;
 
public class Main {

	private static FastReader fr = new FastReader();
	private static Helper helper = new Helper();
	private static StringBuilder result = new StringBuilder();
 
	public static void main(String[] args) {
		Task solver = new Task();
		solver.solve();
	}
 
	static class Task {
	    
		public void solve() {
		    int nt = fr.ni();
			while (nt-- > 0) {
				long n = fr.nl();
				if (n == 1) {
					result.append("FastestFinger\n");
				}
				else if (n == 2 || n % 2 != 0) {
					result.append("Ashishgup\n");
				}
				else{
					if(n % 4 == 0){
						while(n % 2 == 0) n /= 2;
						if(n != 1) result.append("Ashishgup\n");
						else result.append("FastestFinger\n");
					}
					else if(n % 2 == 0){
						n = n/2;
						int count = 0;
						for(int i=3; i<=Math.sqrt(n)+1; i++){
							while(n % i == 0){
								n /= i;
								count++;
							}
						}
						if(n != 1) count++;
						if(count == 1) result.append("FastestFinger\n");
						else result.append("Ashishgup\n");
					}
				}
			}
			System.out.println(result);
		}
	}
    
    static class Helper{
		public long[] tiArr(int n, int si){
			long[] arr = new long[n];
			for(int i=si; i<n; i++) arr[i] = fr.nl();
			return arr;
		}
	}
 
	static class FastReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
		private static PrintWriter pw;
 
		public FastReader() {
			reader = new BufferedReader(new InputStreamReader(System.in));
			pw = new PrintWriter(System.out);
			tokenizer = null;
		}
 
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
 
		public int ni() {
			return Integer.parseInt(next());
		}
 
		public long nl() {
			return Long.parseLong(next());
		}
 
		public String rl() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return null;
		}
 
		public void print(String str) {
			pw.print(str);
			pw.flush();
		}
	}
}