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 sys;
import math;
def get_ints(): return map(int, sys.stdin.readline().strip().split())
def get_array(): return list(map(int, sys.stdin.readline().strip().split()))
def get_string(): return sys.stdin.readline().strip()

def primeFactors(n): 
      
    # Print the number of two's that divide n
    arr = [];
    while n % 2 == 0: 
        arr.append(2);
        n = n // 2
          
    # n must be odd at this point 
    # so a skip of 2 ( i = i + 2) can be used 
    for i in range(3,int(math.sqrt(n))+1,2): 
          
        # while i divides n , print i ad divide n 
        while n % i== 0:
            arr.append(i);
            #print i, 
            n = n // i 
              
    # Condition if n is a prime 
    # number greater than 2 
    if n > 2: 
        #print n
        arr.append(n);
    return list(set(arr))

def getDivisors(n) : 
      

    i = 1
    arr = [];
    while i <= math.sqrt(n): 
          
        if (n % i == 0) : 
              

            if (n // i == i) : 
                arr.append(i) 
            else :
                arr.append(i);
                arr.append(n//i);
        i = i + 1
    return arr;


t = int(input());
for test in range(t):
    n = int(input());
    a = False;
    b = False;
    if(n==2):
        a = True;
        print("Ashishgup");
    if(n==1):
        b = True;
        print("FastestFinger");
    if(a or b):
        continue;
    arr = getDivisors(n);
    pm = primeFactors(n);
    
    #print(pm);
    
    isaval2 = False;
    if 2 in pm:
        isaval2 = True;
    #print(isaval2)
    if(isaval2==False):
        print("Ashishgup");
        continue;
    count = 0;
    while(n%2==0):
        n = n//2;
        count+=1;
    count2 = 0;
    for i in range(len(pm)):
        while(n%pm[i]==0):
            n=n//pm[i];
            count2+=1;
    #print(count,count2)
    if(count==1):
        if(count2>1):
            a=True;
        else:
            b=True;
    else:
        if(count2==0):
            b=True;
        else:
            a=True;
    if(a):
        print("Ashishgup");
    else:
        print("FastestFinger");
    
    
