Uolevi and Maija play a game called HIIT game. In this game, there is initially a string that consists of characters H, I and T. Uolevi starts the game, and the players move alternately. On each move, the player removes any substring "HIIT" from the string. The game ends, when there are no possible moves.

You are given the initial string, and your task is to find out who will win the game if both players play optimally.

Input

The only input line contains a string of length n that consists of characters H, I and T.

Output

Print the winner of the game – "Uolevi" or "Maija".

Constraints

• 1 \le n \le 10^6

Example

Input:

HIHIITIT

Output:

Maija