Alice's Binary Grid Pattern

Alice is fascinated by binary. She believes that only things that have something to do with binary are beautiful. One day, she imagined a pattern and decided to draw it on a grid whose width and height are both 2^n. The grid cells are either black or white, and initially all cells are white.

Alice defines a painting operation as follows: choose a cell; then, that cell and its four neighbors (up, down, left, right) have their colors inverted (black becomes white and white becomes black). Note that the grid is on a torus – the first row and the last row are adjacent, and similarly the first column and the last column are adjacent.

Your task is to either output a sequence of operations to achieve her desired pattern or indicate that it is unsolvable. If there are multiple valid solutions, output any one of them.

Note: The operations you output must transform an all-white grid into the given target pattern. The toggle effect of an operation on a cell is done modulo 2 (i.e. applying the same operation twice cancels out).

inputFormat

The input begins with an integer n on the first line. The grid has size 2^n x 2^n. Following this are 2^n lines, each containing a string of exactly 2^n characters. Each character is either '0' (representing a white cell) or '1' (representing a black cell), which describes the desired target pattern.

outputFormat

If a solution exists, output the number of operations m on the first line, followed by m lines each containing two integers. Each pair of integers (r, c) indicates that you should perform the painting operation on the cell in the r-th row and c-th column (1-indexed). If no solution exists, simply output -1 (without quotes).

sample

1
10
00

1
1 1