A particularly interesting math problem catches your eye! The problem is asking about an ~M~ by ~N~ grid. Some of these squares are coloured black while the rest are white. The grid in this problem is coloured in such a way that no four distinct black squares form a rectangle with sides parallel to the sides of the grid.

You are trying to see what kind of colourings of the ~M~ by ~N~ grid have this property. As such, you have given yourself a colouring of the grid. However, you aren't sure if the way you coloured it actually works.

Given a colouring of an ~M~ by ~N~ grid, determine whether or not there exist four distinct black squares which form a rectangle with sides parallel to the sides of the grid.

Clarification: These four distinct black squares must be exactly the four corners of the rectangle they form.

Constraints

Subtask 1 [20%]

~1 \le M, N \le 70~

Subtask 2 [30%]

~1 \le M, N \le 400~

Subtask 3 [50%]

~1 \le M, N \le 2\,000~

Input Specification

The first line will contain two space-separated integers, ~M~ and ~N~ in that order.
The next ~M~ lines will each contain a single string of length ~N~. Each character will either be a . representing a white tile, or a # representing a black tile.

Output Specification

Output the answer on a single line. This answer should be yes if this colouring does not have a rectangle formed by four black squares. Otherwise, output no.

Sample Input 1

3 4
#.##
##..
..##

Sample Output 1

no

Sample Input 2

1 4
####

Sample Output 2

yes