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 math
def dvisor(n):
    i=1
    l=[]
    while i<=math.sqrt(n):
        if(n%i==0):
            if(n/i==i):
                l.append(i)
            else:
                l.append(i)
                l.append(n//i)
        i+=1
    #print(l)
    return l
def solve(n):
    l1 = dvisor(n)
    #l1.sort()
    #print(l1)
    c = 0
    while (len(l1)>0):
        a = min(l1)
        if (a % 2 != 0 and a != 1):
            c = a
            break
        else:
            del (l1[l1.index(a)])
    return c
for _ in range(int(input())):
    n=int(input())
    if(n==1):
        print('FastestFinger')
        #continue
    elif(n==2):
        print('Ashishgup')
        #continue
    elif(n%2!=0):
        print('Ashishgup')
    else:
        c = solve(n)
        # print(c)
        if (c == 0 and (n - 1) % 2 != 0):
            print('FastestFinger')
            #break
        else:
            n = n // c
            n = n - 1
            if (n % 2 != 0 and n != 1):
                print('Ashishgup')
                #break
            if (n == 1):
                print('FastestFinger')
                #break
        #while(True):
