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C - Counting Squares

Score : $300$ points

Problem Statement

There is a two-dimensional plane. For integers $r$ and $c$ between $1$ and $9$, there is a pawn at the coordinates $(r,c)$ if the $c$-th character of $S_{r}$ is #, and nothing if the $c$-th character of $S_{r}$ is ..

Find the number of squares in this plane with pawns placed at all four vertices.

Constraints

• Each of $S_1,\ldots,S_9$ is a string of length $9$ consisting of # and ..

Input

The input is given from Standard Input in the following format:

$S_1$

$S_2$

$\vdots$

$S_9$

Output

Print the answer.

##.......
##.......
.........
.......#.
.....#...
........#
......#..
.........
.........

2

The square with vertices $(1,1)$, $(1,2)$, $(2,2)$, and $(2,1)$ have pawns placed at all four vertices.

The square with vertices $(4,8)$, $(5,6)$, $(7,7)$, and $(6,9)$ also have pawns placed at all four vertices.

Thus, the answer is $2$.

.#.......
#.#......
.#.......
.........
....#.#.#
.........
....#.#.#
........#
.........

3