p03422 AtCoder Regular Contest 091 - Strange Nim
Takahashi and Aoki are playing a stone-taking game. Initially, there are N piles of stones, and the i-th pile contains A_i stones and has an associated integer K_i.

Starting from Takahashi, Takahashi and Aoki take alternate turns to perform the following operation:

* Choose a pile. If the i-th pile is selected and there are X stones left in the pile, remove some number of stones between 1 and floor(X/K_i) (inclusive) from the pile.



The player who first becomes unable to perform the operation loses the game. Assuming that both players play optimally, determine the winner of the game. Here, floor(x) represents the largest integer not greater than x.

Constraints

* 1 \leq N \leq 200
* 1 \leq A_i,K_i \leq 10^9
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 K_1
:
A_N K_N


Output

If Takahashi will win, print `Takahashi`; if Aoki will win, print `Aoki`.

Examples

Input

2
5 2
3 3


Output

Aoki


Input

3
3 2
4 3
5 1


Output

Takahashi


Input

3
28 3
16 4
19 2


Output

Aoki


Input

4
3141 59
26535 897
93 23
8462 64


Output

Takahashi
```python
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]

def grundy(a,k):
    while 1:
        if a<k:return 0
        if a%k==0:return a//k
        once=a//k+1
        seg=a%k
        cnt=(seg+once-1)//once
        a-=cnt*once

win=0
for _ in range(II()):
    a,k=MI()
    win^=grundy(a,k)

if win:print("Takahashi")
else:print("Aoki")

```