You are given $n + 1$ rods and $3n$ disks. Initially, each of the first $n$ rods contains exactly $3$ disks. Each of the disks has one of $n$ colors (identified by numbers from $1$ to $n$). Moreover, there are exactly $3$ disks of each of the $n$ colors. The $(n + 1)$-th rod is empty. \includegraphics{https://static.e-olymp.com/content/13/13b90f30513a3bb573e8509d519825484d0645d9.gif} At each step we can select two rods $a$ and $b~(a \ne b)$ such that $a$ has at least $1$ disk and $b$ has at most $2$ disks, and move the topmost disk from rod $a$ to the top of rod $b$. Note that no rod is allowed to contain more than $3$ disks at any time. Your goal is to sort the disks. More specifically, you have to do a number of operations (potentially $0$), so that, at the end, each of the first $n$ rods contains exactly $3$ disks of the same color, and the $(n + 1)$-th rod is empty. Find out a solution to sort the disks in at most $6n$ operations. It can be proven that, under this condition, a solution always exists. If there are multiple solutions, any one is accepted. \InputFile The first line contains a positive integer $n~(1 \le n \le 1000)$. The next $3$ lines contain $n$ positive integers $c_{i,j}~(1 \le i \le 3, 1 \le j \le n, 1 \le c_{i,j} \le n)$ each, the color each of the disks initially placed on the rods. The first of the $3$ lines indicates the upper row, the second line indicates the middle row, and the third line indicates the lower row. \OutputFile The first line must contain a non-negative integer $k~(0 \le k \le 6n)$, the number of operations. Each of the following $k$ lines should contain two distinct numbers $a_i, b_i~(1 \le a_i, b_i \le n + 1$, for all $1 \le i \le k)$, representing the $i$-th operation (as described in the statement).