Because MCPT has stolen SAC's idea to sell hotdogs at food day, Zoe decides to bake cookies instead.

Currently, she has an ~N \times M~ baking sheet. This sheet can be thought of as a matrix of cells, with ~(1, 1)~ as the top-left cell and ~(N, M)~ as the bottom-right.

Zoe has placed cookie dough on some cells and has just placed the sheet in the oven. However, she forgets that cookie dough expands when baking. A strange phenomenon happens as a result: if a cell not containing cookie dough is cardinally adjacent (horizontally or vertically) to at least two other cells containing cookie dough, the cookie dough will fill that cell after ~1~ minute.

Fascinated, Zoe wonders how many cells contain cookie (not dough anymore!) if she bakes the cookies for ~K~ minutes.

Constraints

For all subtasks,

~1 \le N, M \le 10^3~

~1 \le K \le 10^9~

Subtask 1 [25%]

~1 \le N, M, K \le 50~

Subtask 2 [75%]

No additional constraints.

Input Specification

The first line will contain ~N~, ~M~, and ~K~, space-separated.

The next ~N~ lines will contain ~M~ O or . characters, denoting whether there is cookie dough at that cell, or not, respectively.

Output Specification

Output a single integer on one line: how many cells contain cookie if she baked the cookies for ~K~ minutes.

Sample Input 1

6 6 10
..O...
.....O
.OO...
......
.....O
....O.

Sample Output 1

11

Explanation for Sample Output 1

The following diagrams describe how the cookie dough expands after ~1~, ~2~, and ~3~ minutes respectively. After three minutes the cookie dough no longer expands, and Zoe is left with ~11~ cells containing cookie.

..O...
..O..O
.OO...
......
....OO
....OO

..O...
.OO..O
.OO...
......
....OO
....OO

.OO...
.OO..O
.OO...
......
....OO
....OO

Sample Input 2

3 2 1
.O
O.
O.

Sample Output 2

5