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.
def cin():
    return map(int, input().split())


# for t in range(int(input())):
#     n, x = cin()
#     a = list(cin())
#     b = sorted(a, reverse=True)
#     ans = 0
#     j = 0
#     for i in range(n):
#         if b[i] * (i - j + 1) >= x:
#             ans += 1
#             j = i + 1
#     print(ans)


# for t in range(int(input())):
#     s = input()
#     n = len(s)
#     pref = [0]
#     l = float('inf')
#     for c in s:
#         pref.append(pref[-1] + (1, -1)[c == '-'])
#         l = min(l, pref[-1])
#     init = max(0, l * -1)
#     ans = 0
#     j = 1
#     for i in range(init):
#         while i + pref[j] >= 0:
#             j += 1
#         ans += j
#         j += 1
#     print(ans + n)


# for t in range(int(input())):
#     n = int(input())
#     a = list(cin())
#     cnt = 0
#     for i in range(n):
#         if a[i] == i + 1:
#             cnt += 1
#     if cnt == n:
#         print(0)
#     else:
#         l, r = 0, 0
#         for i in range(n):
#             if a[i] != i + 1:
#                 l = i
#                 break
#         for i in range(n - 1, -1, -1):
#             if a[i] != i + 1:
#                 r = n - i - 1
#                 break
#         cnt = cnt - l - r
#         if not cnt:
#             print(1)
#         else:
#             print(2)


# for t in range(int(input())):
#     a, b, n, m = cin()
#     if m <= min(a, b) and a + b - m >= n:
#         print('Yes')
#     else:
#         print('No')


# for t in range(int(input())):
#     n, k = cin()
#     a = list(cin())
#     w = list(cin())
#     a.sort()
#     w.sort()
#     ans = 0
#     idx = k
#     for i in range(k):
#         if w[i] > 1:
#             idx = i
#             break
#         ans += a.pop() * 2
#     j = 0
#     for i in range(k - 1, idx - 1, - 1):
#         ans += a.pop() + a[j]
#         j += w[i] - 1
#     print(ans)


def is_prime(x):
    for i in range(3, int(x**0.5) + 1):
        if not x % i:
            return False
    return True


for t in range(int(input())):
    n = int(input())
    if n % 2 and n > 1 or n == 2:
        print('Ashishgup')
    elif n == 1:
        print('FastestFinger')
    else:
        if not n & (n - 1) or n % 4 and is_prime(n // 2):  # is it 2**x
            print('FastestFinger')
        else:
            print('Ashishgup')
