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.*;
 
 
public class Main{
static int mod = (int)(Math.pow(10, 9) + 7);
   public static void main(String[] args) {
      MyScanner sc = new MyScanner();
      out = new PrintWriter(new BufferedOutputStream(System.out));
      int t=  sc.nextInt();
      while (t-->0) {
    	  int n = sc.nextInt();
          if (n == 1) out.println("FastestFinger");
          else if (n == 2) out.println("Ashishgup");
          else if (n == 4) out.println("FastestFinger");
          else if (n % 2 == 1) out.println("Ashishgup");
          else if (n % 4 == 0){
              // if only powers of two ashishgup is screwed
              while (n % 2 == 0) n/=2;
              if (n == 1){
                  out.println("FastestFinger");
              }
              else out.println("Ashishgup");
          }
          else{
              
              // find number of odd prime factors 
                n/=2;
              boolean[] sieve = new boolean[(int)(Math.sqrt(n))+1];
              Arrays.fill(sieve, true);
              sieve[0] = false;
              sieve[1] = false;
              List<Integer> p = new ArrayList<Integer>();
              for (int i = 2; i < sieve.length; i++){
                  if (!sieve[i]) continue;
                  for (int j = i*2; j < sieve.length; j+=i){
                      sieve[j] = false;
                  }
              }
              for (int i = 0; i < sieve.length; i++) {
                  if (sieve[i]) p.add(i);
              }
               
              int numP = 0;
              for (int prime: p){
                  while (n % prime == 0){
                      numP++;
                      n /= prime;
                  }
              }
              if (n > 1) numP++;
              //out.println(numP);
              if (numP <= 1){
                  out.println("FastestFinger");
              }
              else out.println("Ashishgup");
          }
      }
      
      out.close();
   }
   
   static long pow(long a, long N) {
	   if (N == 0) return 1;
	   else if (N == 1) return a;
	   else {
		   long R = pow(a,N/2);
		   if (N % 2 == 0) {
			   return R*R;
		   }
		   else {
			   return R*R*a;
		   }
	   }
   }
   
   static long powMod(long a, long N) {
	   if (N == 0) return 1;
	   else if (N == 1) return a % mod;
	   else {
		   long R = powMod(a,N/2) % mod;
		   R *= R % mod;
		   if (N % 2 == 1) {
			   R *= a % mod;
		   }
			   return R % mod;
	   }
   }
static void mergeSort(int[] A){ // low to hi sort, single array only
      int n = A.length;
      if (n < 2) return;
      int[] l = new int[n/2];
      int[] r = new int[n - n/2];
 
      for (int i = 0; i < n/2; i++){
        l[i] = A[i];
      }
 
      for (int j = n/2; j < n; j++){
        r[j-n/2] = A[j];
      }
 
      mergeSort(l);
      mergeSort(r);
      merge(l, r, A);
    }
 
    static void merge(int[] l, int[] r, int[] a){
      int i = 0, j = 0, k = 0;
      while (i < l.length && j < r.length && k < a.length){
        if (l[i] < r[j]){
          a[k] = l[i];
          i++;
        }
        else{
          a[k] = r[j];
          j++;
        }
        k++;
      }
      while (i < l.length){
        a[k] = l[i];
        i++;
        k++;
      }
 
      while (j < r.length){
        a[k] = r[j];
        j++;
        k++;
      }
    }

   

   //-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         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;
      }

   }
   //--------------------------------------------------------
}







