Grid Path Finder

You are given a grid with m rows and n columns. Each cell in the grid contains an integer value. Your task is to determine if there exists a valid path from the top-left corner to the bottom-right corner.

You can only move in two directions: right or down. However, you can only move from a cell with value \(A_{i,j}\) to an adjacent cell if the value of the target cell is not less than \(A_{i,j}\) (i.e. \(A_{next} \geq A_{current}\)).

If such a path exists, output YES; otherwise, output NO.

inputFormat

The input is given via standard input and has the following format:

The first line contains two integers m and n separated by a space.

This is followed by m lines, each containing n space-separated integers representing the grid.

outputFormat

Output a single string to the standard output: either YES if there exists a valid path based on the rules, or NO if no such path exists.## sample

3 3
1 2 3
6 5 2
7 6 8

YES