Rectangular Path Check

You are given a grid of n rows and m columns, where each cell contains either '1' or '0'. Your task is to determine whether there exists a rectangle in the grid such that all four corners of the rectangle are '1'.

A rectangle is defined by two distinct rows r₁ and r₂ (with r₁ < r₂) and two distinct columns c₁ and c₂ (with c₁ < c₂). The rectangle's corners are located at positions (r₁, c₁), (r₁, c₂), (r₂, c₁) and (r₂, c₂). The answer is "Yes" if such a rectangle exists, otherwise "No".

In mathematical terms, you need to check if there exist indices r₁, r₂, c₁, c₂ such that:

$$\text{grid}[r_1][c_1] = \text{grid}[r_1][c_2] = \text{grid}[r_2][c_1] = \text{grid}[r_2][c_2] = '1' $$

inputFormat

The first line contains two integers n and m, separated by a space — the number of rows and columns in the grid.

Each of the next n lines contains a string of length m composed of characters '0' and '1', representing a row of the grid.

outputFormat

Output a single line containing either "Yes" if there exists a rectangle whose four corners are all '1', or "No" otherwise.

## sample

4 5
11011
11011
11111
01110

Yes