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.
"""
NTC here
"""
 
 
#!/usr/bin/env python
import os
import sys
from io import BytesIO, IOBase

profile = 0
pypy = 1
 
 
def iin(): return int(input())


def lin(): return list(map(int, input().split()))


def factors(a):
    fact = []
    if a % 2 == 0:
        ch = 0
        while a % 2 == 0:
            ch += 1
            a //= 2
        fact.append([2, ch])
    i = 3
    while i*i <= a:
        if a % i == 0:
            ch = 0
            while a % i == 0:
                ch += 1
                a //= i
            fact.append([i, ch])
        i += 2
    if a > 1:
        fact.append([a, 1])
    return fact

def main():
    ans = ["FastestFinger", "Ashishgup" ]
    T = iin()
    while T:
        T -= 1
        n = iin()
        ch = 0
        while n>1:
            ch += 1
            ch1 = 0
            if n%2:
                break
            while n%2==0:
                ch1 += 1
                n//=2
            # print('t1', n)
            if ch1>1:
                ch += 1
            
            f = factors(n)
            # print('t2', f)
            if f:
                ch1 = 0
                for i, j in f:
                    ch1 += j
                if ch==2:
                    ch += 1
                else:
                    if ch1>1:
                        ch += 2
                        break
                    else:
                        ch += 1
                        break
            break
        
        print(ans[ch%2])
                        





    




                

        

 
 
 
 
 
 
# region fastio
 
BUFSIZE = 8192
 
 
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
 
 
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
 
if pypy:
    sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
    input = lambda: sys.stdin.readline().rstrip("\r\n")
 
# endregion
 
if __name__ == "__main__":
    if profile:
        import cProfile
        cProfile.run('main()')
    else:
        main()