Counting Islands

New Zealand is a country located in the southwestern Pacific Ocean, comprising of about 600 islands. However, there are only two main islands.

Given a map of an arbitrary ocean, determing how many main islands (islands with area not less than some threshold $T$) are in it.

Input

The first line of input contains three integers, $W$, $H$, and $T$ ($1 \leq W, H \leq 1000, 1 \leq T \leq W \times H$), describing the width and height of the map in kilometers and the threshold for main island status in square kilometers, respectively.

The following $H$ lines each contain $W$ characters, representing the map of ocean. A # character denotes a square kilometer of land, and a . character denotes a square kilometer of ocean. Islands do not connect diagonally.

Output

Output should be a single line with a single integer - the number of main islands depicted in the map.

Subtasks

The following subtasks are available:

• Subtask 1 ($20\%$): Every island has an area of $1$ square kilometer; is represented by a single # character
• Subtask 2 ($20\%$): $W, H \leq 20$
• Subtask 3 ($60\%$): No further restrictions