Problem

One day, mo3tthi and tubuann decided to play a game with magic pockets and biscuits.
Now there are $ K $ pockets, numbered $1,2, \ ldots, K$.
The capacity of the $ i $ th pocket is $ M_i $, which initially contains $ N_i $ biscuits.
mo3tthi and tubuann start with mo3tthi and perform the following series of operations alternately.

• Choose one pocket.
• Perform one of the following operations only once. However, if the number of biscuits in the pocket selected as a result of the operation exceeds the capacity of the pocket, the operation cannot be performed.
• Stroking the selected pocket. Magical power increases the number of biscuits in your chosen pocket by $ 1 $.
• Hit the selected pocket. The number of biscuits in the pocket chosen by magical power is doubled by $ 2 $.

The game ends when you can't operate it, the person who can't operate loses, and the person who doesn't can win.
You, a friend of mo3tthi, were asked by mo3tthi in advance if you could decide if you could win this game.
For mo3tthi, make a program to determine if mo3tthi can definitely win this game.

Constraints

The input satisfies the following conditions.

• $1 \ leq K \ leq 10 ^ 5$
• $1 \ leq N_i \ leq M_i \ leq 10 ^ {18}$
• All inputs are integers

Input

The input is given in the following format.

$ K $
$ N_1 $ $ M_1 $
$\$
$ N_K $ $ M_K $

Output

When mo3tthi acts optimally, "mo3tthi" is output on one line if he can win, and "tubuann" is output otherwise.

Examples

Input

1
2 4

Output

mo3tthi

Input

2
2 3
3 8

Output

tubuann

Input

10
2 8
5 9
7 20
8 41
23 48
90 112
4 5
7 7
2344 8923
1 29

Output

mo3tthi

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