K. Party Games
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

After finally rounding up the Fluttershies at Sweet Apple Acres, we made our way to Pinkie Pie's Sugarcube Corner.

"Wheee!!! Fluttershies, let's have a party!"

There was no way around it; we had to join in and play with Pinkie Pie.

Pinkie Pie invented a two-player game, and we took turns challenging her. Specifically, the game goes as follows:

There are $$$n$$$ integers $$$1,2,3,\dots,n$$$​ arranged in a row from left to right. Both Pinkie Pie and I will take turns trying the following operation:

  • If the bitwise XOR sum of the remaining integers is not $$$0$$$​, remove either the leftmost or the rightmost integer from the row without changing the order of the remaining numbers.

If the current player cannot make a move, they lose the game.

The game consists of $$$T$$$ rounds, assuming "I"$$$\ $$$always starts first each round, and both of us aim for victory by making optimal moves. The question is whether "I"$$$\ $$$can achieve victory in each round of the game.

The bitwise XOR sum of several numbers $$$a_1,a_2,\dots,a_m$$$ is denoted by $$$a_1 \oplus a_2 \oplus \dots \oplus a_m$$$. Particularly, the XOR sum of an empty set is $$$0$$$.

The XOR operation, denoted by $$$\oplus$$$, is a binary operation that compares two binary numbers bit by bit. At each position, if the corresponding bits are not all $$$1$$$ or not all $$$0$$$, the result is $$$1$$$; otherwise, it's $$$0$$$.

Input

The first line contains an integer $$$T$$$ ($$$1 \leq T \leq 10^5$$$), indicating the number of rounds in the game.

Following that are $$$T$$$ lines, each containing an integer $$$n$$$ ($$$1 \leq n \leq 10^6$$$), representing the number of integers in the corresponding round of the game.

Output

For each round of the game, output one line. If "I"$$$\ $$$can win, output "Fluttershy"; otherwise, output "Pinkie Pie" (without the quotes).

Example
Input
3
1
2
3
Output
Fluttershy
Pinkie Pie
Pinkie Pie
Note

In the first example, "I"$$$\ $$$choose to take $$$1$$$, leaving Pinkie Pie unable to make a move. Thus, "I"$$$\ $$$win.

In the second example, regardless of whether "I"$$$\ $$$choose to take $$$1$$$ or $$$2$$$, Pinkie Pie can always take the remaining numbers, rendering "I"$$$\ $$$unable to make a move and lose the game.

In the third example, the initial XOR sum is already $$$0$$$, so "I"$$$\ $$$cannot make a move and lose the game.