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.
"""
Code of Ayush Tiwari
Codeforces: servermonk
Codechef: ayush572000

"""
import sys
input = sys.stdin.buffer.readline

def solution():
    for _ in range(int(input())):
        
        # This is the main code
        flag=0
        cnt=0
        n=int(input())
        if n==1:
            print('FastestFinger')
        elif n%2!=0:
            print('Ashishgup')
        else:
            while n>=2:
                d=[]
                if n==1:
                    if cnt%2!=0:
                        print('Ashishgup')
                    else:
                        print('FastestFinger')
                    break
                if n%2==0:
                    for i in range(2,int(n**0.5)+1): 
                        if n%i==0:
                            y=n//i
                            if i%2!=0:
                                d.append(i)
                                flag=1
                            if y%2!=0:
                                d.append(y)
                    
                    if d==[]:
                        if n==2:
                            if cnt%2==0:
                                print('Ashishgup')
                            else:
                                print('FastestFinger')
                        elif cnt%2!=0:
                            print('Ashishgup')
                        else:
                            print('FastestFinger')
                        break
                    else:
                        d.sort()
                        ma=d[-1]
                        m=d[len(d)-2]
                        # print(ma,m)
                        if n//ma==2:
                            n//=m
                            # print(n)
                        else:
                            n//=ma
                            # print(n)
                    cnt+=1
                else:
                    if cnt%2==0:
                        print('Ashishgup')
                    else:
                        print('FastestFinger')
                    break
solution()