Valid Rainbow Pattern Checker

You are given a grid of size \(n \times m\) filled with integers. Your task is to determine whether the grid forms a valid rainbow pattern. The grid is said to form a valid rainbow pattern if:

• Every row is in non-decreasing order.
• Every column is in non-decreasing order.
• The grid contains all distinct integers from \(1\) to \(n \times m\) exactly once.

Print YES if all conditions are satisfied, otherwise print NO.

Note: The input is provided via stdin and the output must be printed to stdout.

inputFormat

The first line contains two integers \(n\) and \(m\), representing the number of rows and columns respectively. The following \(n\) lines each contain \(m\) space-separated integers representing the grid.

It is guaranteed that \(1 \leq n, m \leq 100\) and the integers in the grid are between \(1\) and \(n \times m\).

outputFormat

Output a single line containing YES if the grid forms a valid rainbow pattern, otherwise output NO.

4 3
1 2 3
4 5 6
7 8 9
10 11 12

YES