Balanced Garden

You are given a garden represented as a grid with N rows and M columns. Each cell of the grid contains an integer:

• 0 represents a flower.
• 1 represents a river.

A garden is considered balanced if for every flower (cell with 0), there exists at least one adjacent cell (vertically or horizontally) that contains a river (1). In mathematical terms, for every cell \( (i,j) \) with \( grid[i][j]=0 \), there must exist an adjacent cell \( (i',j') \) (where \( |i-i'|+|j-j'|=1 \)) such that \( grid[i'][j']=1 \).

Your task is to determine if the garden is balanced. Print YES if it is balanced, otherwise print NO.

inputFormat

The input is read from standard input and has the following format:

N M
row1
row2
... 
rowN

Here, the first line contains two integers N and M representing the number of rows and columns in the garden respectively. The next N lines each contain M space-separated integers (each either 0 or 1) representing the grid.

outputFormat

Output a single line to standard output: YES if the garden is balanced according to the given definition, otherwise NO.

3 3
0 1 0
1 0 1
0 1 0

YES