Transforming a Grid into a Latin Square

You are given an n × n grid in which each row is a permutation of the integers from 1 to n. Your task is to transform the grid into a Latin square by performing a sequence of operations. In a Latin square, every row and every column contains each integer from 1 to n exactly once.

You are allowed to perform the following operations:

• row x y: Swap row x with row y (1-indexed).
• column x y: Swap column x with column y (1-indexed).

The objective is to use as few operations as possible. Note that if the grid is already a Latin square, you should output 0 operations. Also, note that it is only possible to transform the grid into a Latin square if each row and each column (when viewed as a multiset) is exactly equal to {1, 2, …, n}.

Warning: The input is provided such that it is always possible to get a Latin square through row and column swaps.

inputFormat

The first line contains an integer n (1 ≤ n ≤ 50) — the size of the grid. The following n lines each contain n integers separated by spaces, representing the grid. It is guaranteed that each row is a permutation of the integers from 1 to n, and the grid is transformable into a Latin square by row and column swaps.

outputFormat

On the first line, print an integer q (0 ≤ q ≤ 1000) representing the number of operations performed. Then print q lines, each describing one operation in one of the following forms:

• row x y — indicating a swap of row x with row y.
• column x y — indicating a swap of column x with column y.

If the grid is already a Latin square, your program should output 0 and nothing more.

## sample

4
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3

0

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