9129: ABC330 —— D - Counting Ls
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Description
You are given an $N \times N$ grid. Let $(i,j)$ denote the cell in the $i$\-th row from the top and the $j$\-th column from the left.
The states of the cells are given by $N$ strings of length $N$, $S_1, S_2, \dots, S_N$, in the following format:
- If the $j$\-th character of $S_i$ is `o`, there is an `o` written in cell $(i,j)$.
- If the $j$\-th character of $S_i$ is `x`, there is an `x` written in cell $(i,j)$.
Find the number of triples of cells that satisfy all of the following conditions:
- The three cells in the triple are distinct.
- All three cells have an `o` written in them.
- Exactly two of the cells are in the same row.
- Exactly two of the cells are in the same column.
Here, two triples are considered different if and only if some cell is contained in exactly one of the triples.
The states of the cells are given by $N$ strings of length $N$, $S_1, S_2, \dots, S_N$, in the following format:
- If the $j$\-th character of $S_i$ is `o`, there is an `o` written in cell $(i,j)$.
- If the $j$\-th character of $S_i$ is `x`, there is an `x` written in cell $(i,j)$.
Find the number of triples of cells that satisfy all of the following conditions:
- The three cells in the triple are distinct.
- All three cells have an `o` written in them.
- Exactly two of the cells are in the same row.
- Exactly two of the cells are in the same column.
Here, two triples are considered different if and only if some cell is contained in exactly one of the triples.
Input
The input is given from Standard Input in the following format:
```
$N$
$S_1$
$S_2$
$\vdots$
$S_N$
```
```
$N$
$S_1$
$S_2$
$\vdots$
$S_N$
```
Output
Print the answer as an integer.
Constraints
- $N$ is an integer between $2$ and $2000$, inclusive.
- $S_i$ is a string of length $N$ consisting of `o` and `x`.
- $S_i$ is a string of length $N$ consisting of `o` and `x`.
Sample 1 Input
3
ooo
oxx
xxo
Sample 1 Output
4
The following four triples satisfy the conditions:
- (1,1),(1,2),(2,1)
- (1,1),(1,3),(2,1)
- (1,1),(1,3),(3,3)
- (1,2),(1,3),(3,3)
Sample 2 Input
4
oxxx
xoxx
xxox
xxxo
Sample 2 Output
0
Sample 3 Input
15
xooxxooooxxxoox
oxxoxoxxxoxoxxo
oxxoxoxxxoxoxxx
ooooxooooxxoxxx
oxxoxoxxxoxoxxx
oxxoxoxxxoxoxxo
oxxoxooooxxxoox
xxxxxxxxxxxxxxx
xooxxxooxxxooox
oxxoxoxxoxoxxxo
xxxoxxxxoxoxxoo
xooxxxooxxoxoxo
xxxoxxxxoxooxxo
oxxoxoxxoxoxxxo
xooxxxooxxxooox
Sample 3 Output
2960
HINT
相同题目：ABC330。