A. Extreme Grid Game
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Munir and Matthew are playing a high-stakes game on an $$$n\times m$$$ grid. They take turns placing rectangles of size at most $$$k$$$ on the board. It is not allowed to place rectangles that overlap with an existing rectangle on the board. The first player who is unable to place a rectangle loses.

Assuming both players play optimally, with Munir playing first, who wins?

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t\ (1\le t\le 10^3)$$$. The description of the test cases follows.

The only line of each test case contains three integers $$$n, m, k\ (1\le n,m\le 10^3, 1\le n\cdot m\le 10^3, 1\le k\le n\cdot m)$$$.

It is guaranteed the sum of $$$n\times m$$$ over all test cases does not exceed $$$10^3$$$

Output

For each test case, print 'Munir' (without quotes) if Munir wins. Otherwise, print 'Matthew'.

Example
Input
3
2 3 1
3 3 4
3 4 6
Output
Matthew
Munir
Munir
Note

In the third sample case, one way Munir can win is by playing a $$$3\times 2$$$ rectangle to split the board into two halves.