Practice Graph traversal with the exercise "We're going in circles!"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

graph traversal

Statement

Goal

There is a w by h grid of arrows represented by: "^", ">", "v", "<". Empty cells are represented by periods: ".".

A loop of arrows is a set of arrows that loop back on themselves when moving from one arrow to the closest arrow in the direction that it points. If an arrow points outside the grid, it is not part of a loop.

The goal is to count the number_of_loops in the grid.

Input

line 1: w and h separated by a space (width and height, respectively).
The next h lines: The grid of arrows and empty cells.

Output

The number_of_loops in the grid.

Constraints

0 < w, h <= 20
The grid only contains the characters: ^>v<.

Example

Input

5 4
>.>.v
....v
....v
^<<<<

Output

Solve it

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