Double or Increment

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.

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

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

inputFormat

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.

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

outputFormat

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

样例

1
2 4

mo3tthi