Grid Sort

Each cell of a $2 \times N$ grid contains exactly one of the integers $1,2,\ldots,2N$.

Your goal is to make the grid

using the following operations.

• $1\ c$: swap $(1,c)$ and $(1,c+1)$.
• $2\ c$: swap and .

Print a sequence of operations that reaches the target grid. You may receive a partial score depending on the number of operations you output.

The input is given from Standard Input in the following format:

$N$ $A_{1,1}\ A_{1,2}\ \cdots\ A_{1,N}$

Let $M$ be the number of operations. Print your answer in the following format:

$M$ $t_1\ c_1$

• $1 \le N \le 500$.
• $(A_{1,1},A_{1,2},\ldots,A_{1,N},A_{2,1},A_{2,2},\ldots,A_{2,N})$ is a permutation of .

For each judge case, suppose your output is valid and uses $M$ operations. The score for that case is as follows.