| Problem | |
| There are $N$ balls numbered from $1$ to $N$, and three baskets numbered from $1$ to $3$. Initially, all $N$ balls are in basket $1$. | |
| Balls can be moved from one basket to another according to the following rules: | |
| When the balls in a basket are arranged in numerical order, the ball in the middle is called the center ball. | |
| If the number of balls is even, the center ball is the one with the larger number between the two middle balls. | |
| When moving a ball from basket $a$ to basket $b$, the center ball of basket $a$ must be moved to basket $b$, and the moved ball must become the center ball of basket $b$. | |
| Using this rule, output the process of moving all $N$ balls from basket $1$ to basket $3$. | |
| Input | |
| The first line contains the number of balls $N$. ($1 \le N \le 30$) | |
| Output | |
| The first line should output the number of moves $M$. | |
| The next $M$ lines should each contain two integers $a$ and $b$, separated by a space. ($1 \le a, b \le 3; a \ne b$) This indicates that the $i$-th operation moves a ball from basket $a$ to basket $b$ according to the problem's rules. | |
| After the output, all balls originally in basket $1$ must be moved to basket $3$. |