Algorithms and Data Structures

Does the Grid Contain a Cycle?

Given a grid with height h and width w filled with letters, you are allowed to walk on the same letters only. By walking on the same letters (only stepping on letters a or only stepping on letters b, etc) you are wondering if it would be possible to walk and appear on an already visited cell. Note that you're not allowed to move to the previous cell. You are allowed to only walk in horizontal or vertical directions to the neighbor cells.
In other words, you are wondering if there is a cycle of the same letters in the given grid.

Input

The first line of the input contains two integers h and w (1 ≤ h, w ≤ 200).
The next h lines contain w alphabetic characters lowercase Latin letters.

Output

The program should print Yes if the grid has a cycle and No otherwise.

Examples

Input
Output
4 4 aaaa abba abbc aaaa
Yes
4 4 aaaa abba abdc aaaa
No
4 4 aaaa abba abda aaaa
Yes
4 4 ccca cdcc ccec fccc
Yes
3 3 abb bcb bba
No
 

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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