Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. What Has Dirichlet Got to Do with That?

time limit per test

2 secondsmemory limit per test

64 megabytesinput

standard inputoutput

standard outputYou all know the Dirichlet principle, the point of which is that if *n* boxes have no less than *n* + 1 items, that leads to the existence of a box in which there are at least two items.

Having heard of that principle, but having not mastered the technique of logical thinking, 8 year olds Stas and Masha invented a game. There are *a* different boxes and *b* different items, and each turn a player can either add a new box or a new item. The player, after whose turn the number of ways of putting *b* items into *a* boxes becomes no less then a certain given number *n*, loses. All the boxes and items are considered to be different. Boxes may remain empty.

Who loses if both players play optimally and Stas's turn is first?

Input

The only input line has three integers *a*, *b*, *n* (1 ≤ *a* ≤ 10000, 1 ≤ *b* ≤ 30, 2 ≤ *n* ≤ 10^{9}) — the initial number of the boxes, the number of the items and the number which constrains the number of ways, respectively. Guaranteed that the initial number of ways is strictly less than *n*.

Output

Output "Stas" if Masha wins. Output "Masha" if Stas wins. In case of a draw, output "Missing".

Examples

Input

2 2 10

Output

Masha

Input

5 5 16808

Output

Masha

Input

3 1 4

Output

Stas

Input

1 4 10

Output

Missing

Note

In the second example the initial number of ways is equal to 3125.

- If Stas increases the number of boxes, he will lose, as Masha may increase the number of boxes once more during her turn. After that any Stas's move will lead to defeat.
- But if Stas increases the number of items, then any Masha's move will be losing.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/24/2019 06:34:34 (e1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|