Problem Statement

kevin is playing a certain game.
You are given a field consisting of cells, \(W\) wide and \(H\) tall.
You first select a cell, then you can trace only through the same number in the up, down, left and right directions, and you can release at any location.
In this game, you get a high score if you can form an enclosure by tracing only through the same number.

An enclosure means that a \(K( \geq 4)\)-sided polygon is formed when lines are drawn connecting the traced cells in the order they were traced.

Given the field, determine whether an enclosure can be formed.
Output \(possible\) if an enclosure can be formed, and \(impossible\) otherwise.

Input

\(W\ H\)
\(M_{11}\ \dots\ M_{i1}\ \dots\ M_{W1}\)
\(M_{12}\ \dots\ M_{i2}\ \dots\ M_{W2}\)
\(\dots\)
\(M_{1j}\ \dots\ M_{ij}\ \dots\ M_{Wj}\)
\(\dots\)
\(M_{1H}\ \dots\ M_{iH}\ \dots\ M_{WH}\)

Line \(1\) contains the numbers \(W\ (1 \leq W \leq 100) \), representing the width, and \(H\ (1 \leq H \leq 100)\), representing the height, separated by a single-byte space.
From line \(2\) onward, each line contains the numbers \(M_{ij}\ (1 \leq M_{ij} \leq 1000)\), representing column \(i\) of row \(j\), separated by single-byte spaces.

Output

Output possible or impossible.
Print a newline at the end.

Sample

3 3
1 2 3
1 1 3
1 1 4

possible

5 4
1 2 2 2 3
2 2 4 2 2
2 1 1 1 2
2 2 2 2 2

possible

5 4
5 5 5 3 5
5 3 1 5 1
5 2 2 5 8
5 5 5 5 9

impossible