问题

### Instructions: You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. You will NOT return anything except for the program.
### Question:
There is a grid with H rows and W columns. Let (i, j) denote the cell at the i-th row from the top and the j-th column from the left.
Each cell contains one of the characters o, x, and .. The characters written in each cell are represented by H strings S_1, S_2, \ldots, S_H of length W; the character written in cell (i, j) is the j-th character of the string S_i.
For this grid, you may repeat the following operation any number of times, possibly zero:

- Choose one cell with the character . and change the character in that cell to o.

Determine if it is possible to have a sequence of K horizontally or vertically consecutive cells with o written in all cells (in other words, satisfy at least one of the following two conditions). If it is possible, print the minimum number of operations required to achieve this.

- There is an integer pair (i, j) satisfying 1 \leq i \leq H and 1 \leq j \leq W-K+1 such that the characters in cells (i, j), (i, j+1), \ldots, (i, j+K-1) are all o.
- There is an integer pair (i, j) satisfying 1 \leq i \leq H-K+1 and 1 \leq j \leq W such that the characters in cells (i, j), (i+1, j), \ldots, (i+K-1, j) are all o.

Input

The input is given from Standard Input in the following format:
H W K
S_1
S_2
\vdots
S_H

Output

If it is impossible to satisfy the condition in the problem statement, print -1. Otherwise, print the minimum number of operations required to do so.

Constraints


- H, W, and K are integers.
- 1 \leq H
- 1 \leq W
- H \times W \leq 2 \times 10^5
- 1 \leq K \leq \max\lbrace H, W \rbrace
- S_i is a string of length W consisting of the characters o, x, and ..

Sample Input 1

3 4 3
xo.x
..o.
xx.o

Sample Output 1

2

By operating twice, for example, changing the characters in cells (2, 1) and (2, 2) to o, you can satisfy the condition in the problem statement, and this is the minimum number of operations required.

Sample Input 2

4 2 3
.o
.o
.o
.o

Sample Output 2

0

The condition is satisfied without performing any operations.

Sample Input 3

3 3 3
x..
..x
.x.

Sample Output 3

-1

It is impossible to satisfy the condition, so print -1.

Sample Input 4

10 12 6
......xo.o..
x...x.....o.
x...........
..o...x.....
.....oo.....
o.........x.
ox.oox.xx..x
....o...oox.
..o.....x.x.
...o........

Sample Output 4

3

### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows.
```python
# YOUR CODE HERE
```

### Answer: (use the provided format with backticks)

答案

模型 模型答案 正确答案
金声玉亮2.0 ```python
import sys
input = sys.stdin.read
data = input().split()

H = int(data[0])
W = int(data[1])
K = int(data[2])

grid = []
for i in range(H):
grid.append(data[i + 3])

def min_operations(grid, H, W, K):
min_ops = float('inf')

# Check horizontal sequences
for i in range(H):
for j in range(W - K + 1):
ops = 0
for k in range(K):
if grid[i][j + k] != 'o':
if grid[i][j + k] == '.':
ops += 1
else:
ops = float('inf')
break
min_ops = min(min_ops, ops)

# Check vertical sequences
for j in range(W):
for i in range(H - K + 1):
ops = 0
for k in range(K):
if grid[i + k][j] != 'o':
if grid[i + k][j] == '.':
ops += 1
else:
ops = float('inf')
break
min_ops = min(min_ops, ops)

return min_ops if min_ops != float('inf') else -1

print(min_operations(grid, H, W, K))
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
deepseek-r1

```python
import bisect

H, W, K = map(int, input().split())
grid = [input().strip() for _ in range(H)]

# Precompute rows data
pre_sum_rows = []
x_positions_rows = []
for row in grid:
n = len(row)
pre_sum = [0] * (n + 1)
x_pos = []
for i in range(n):
pre_sum[i+1] = pre_sum[i] + (1 if row[i] == '.' else 0)
if row[i] == 'x':
x_pos.append(i)
pre_sum_rows.append(pre_sum)
x_positions_rows.append(x_pos)

# Precompute columns data
pre_sum_cols = []
x_positions_cols = []
for j in range(W):
col = []
x_pos = []
for i in range(H):
c = grid[i][j]
col.append(c)
if c == 'x':
x_pos.append(i)
pre_sum = [0] * (H + 1)
for i in range(H):
pre_sum[i+1] = pre_sum[i] + (1 if col[i] == '.' else 0)
pre_sum_cols.append(pre_sum)
x_positions_cols.append(x_pos)

min_ops = float('inf')

# Check horizontal sequences
for i in range(H):
x_pos = x_positions_rows[i]
pre_sum = pre_sum_rows[i]
max_j = W - K
if max_j < 0:
continue
for j in range(max_j + 1):
start, end = j, j + K - 1
idx = bisect.bisect_left(x_pos, start)
if idx < len(x_pos) and x_pos[idx] <= end:
continue
current_ops = pre_sum[end + 1] - pre_sum[start]
if current_ops < min_ops:
min_ops = current_ops

# Check vertical sequences
for j in range(W):
x_pos = x_positions_cols[j]
pre_sum = pre_sum_cols[j]
max_i = H - K
if max_i < 0:
continue
for i in range(max_i + 1):
start, end = i, i + K - 1
idx = bisect.bisect_left(x_pos, start)
if idx < len(x_pos) and x_pos[idx] <= end:
continue
current_ops = pre_sum[end + 1] - pre_sum[start]
if current_ops < min_ops:
min_ops = current_ops

print(min_ops if min_ops != float('inf') else -1)
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
gpto1 ```python
# YOUR CODE HERE
import sys
import threading

def main():
import sys
import math
sys.setrecursionlimit(1<<25)
H, W, K = map(int, sys.stdin.readline().split())
S = [sys.stdin.readline().strip() for _ in range(H)]

min_ops = None
# Process horizontal sequences if K <= W
if K <= W:
for i in range(H):
A_row_x = [1 if c == 'x' else 0 for c in S[i]]
A_row_dot = [1 if c == '.' else 0 for c in S[i]]
prex_x = [0] * (W + 1)
prex_dot = [0] * (W + 1)
for j in range(W):
prex_x[j+1] = prex_x[j] + A_row_x[j]
prex_dot[j+1] = prex_dot[j] + A_row_dot[j]
for j in range(W - K + 1):
x_count = prex_x[j+K] - prex_x[j]
if x_count == 0:
dot_count = prex_dot[j+K] - prex_dot[j]
if min_ops is None or dot_count < min_ops:
min_ops = dot_count
# Process vertical sequences if K <= H
if K <= H:
for j in range(W):
A_col_x = [1 if S[i][j] == 'x' else 0 for i in range(H)]
A_col_dot = [1 if S[i][j] == '.' else 0 for i in range(H)]
prex_x = [0] * (H + 1)
prex_dot = [0] * (H + 1)
for i in range(H):
prex_x[i+1] = prex_x[i] + A_col_x[i]
prex_dot[i+1] = prex_dot[i] + A_col_dot[i]
for i in range(H - K + 1):
x_count = prex_x[i+K] - prex_x[i]
if x_count == 0:
dot_count = prex_dot[i+K] - prex_dot[i]
if min_ops is None or dot_count < min_ops:
min_ops = dot_count
if min_ops is None:
print(-1)
else:
print(min_ops)


if __name__ == '__main__':
threading.Thread(target=main).start()
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
gpt-4o-2024-08-06 ```python
# YOUR CODE HERE
def min_operations_to_consecutive_o(H, W, K, grid):
# Function to calculate the minimum operations needed for a horizontal sequence
def min_operations_horizontal():
min_ops = float('inf')
for i in range(H):
for j in range(W - K + 1):
# Count the number of '.' in the current K-length horizontal segment
ops = 0
for l in range(K):
if grid[i][j + l] == '.':
ops += 1
min_ops = min(min_ops, ops)
return min_ops

# Function to calculate the minimum operations needed for a vertical sequence
def min_operations_vertical():
min_ops = float('inf')
for j in range(W):
for i in range(H - K + 1):
# Count the number of '.' in the current K-length vertical segment
ops = 0
for l in range(K):
if grid[i + l][j] == '.':
ops += 1
min_ops = min(min_ops, ops)
return min_ops

# Calculate the minimum operations for both horizontal and vertical sequences
min_ops_horizontal = min_operations_horizontal()
min_ops_vertical = min_operations_vertical()

# If both are infinite, it means it's impossible to form such a sequence
if min_ops_horizontal == float('inf') and min_ops_vertical == float('inf'):
return -1

# Return the minimum of the two
return min(min_ops_horizontal, min_ops_vertical)

# Read input
import sys
input = sys.stdin.read
data = input().split()

H = int(data[0])
W = int(data[1])
K = int(data[2])
grid = data[3:H+3]

# Get the result
result = min_operations_to_consecutive_o(H, W, K, grid)

# Print the result
print(result)
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
Qwen2-72B-Instruct ```python
from itertools import groupby
import sys
input = sys.stdin.readline

def main():
H, W, K = map(int, input().split())
S = [list(input().strip()) for _ in range(H)]

def check(arr):
ans = float('inf')
for i in range(len(arr)):
cnt = 0
for j in range(i, len(arr)):
if arr[j][0] == 'o':
continue
else:
cnt += 1
if j-i+1 < K:
continue
if all(x[0] == 'o' for x in zip(*arr[i:j+1])):
ans = min(ans, cnt)
return ans if ans != float('inf') else -1

ans = float('inf')
for bit in range(1 << H):
arr = []
for i in range(H):
if bit & (1 << i):
arr.append(S[i])
if len(arr) < K:
continue
ans = min(ans, check(arr))

for bit in range(1 << W):
arr = []
for i in range(W):
if bit & (1 << i):
arr.append([s[i] for s in S])
if len(arr) < K:
continue
ans = min(ans, check(arr))

print(ans)
```
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
DeepSeek-Coder-V2-Lite-Instruct ```python
# YOUR CODE HERE
import sys

def read_ints():
return list(map(int, sys.stdin.readline().strip().split()))

def read_strings():
return sys.stdin.readline().strip().split()

H, W, K = read_ints()
grid = [sys.stdin.readline().strip() for _ in range(H)]

# Initialize the minimum operations to a large number
min_operations = float('inf')

# Check horizontally
for i in range(H):
for j in range(W - K + 1):
if all(grid[i][j + k] == 'o' for k in range(K)):
min_operations = 0
break

# Check vertically
for j in range(W):
for i in range(H - K + 1):
if all(grid[i + k][j] == 'o' for k in range(K)):
min_operations = 0
break

# If already satisfied, no operations are needed
if min_operations == 0:
print(0)
sys.exit()

# Try to satisfy the condition by changing '.' to 'o'
for i in range(H):
for j in range(W):
if grid[i][j] == '.':
operations = 0
# Check horizontally
for k in range(K):
if grid[i][j + k] == 'o':
break
else:
operations += 1
for k in range(K):
if grid[i][j + k] == '.':
grid[i] = grid[i][:j + k] + 'o' + grid[i][j + k + 1:]
# Check vertically
for k in range(K):
if grid[i + k][j] == 'o':
break
else:
operations += 1
for k in range(K):
if grid[i + k][j] == '.':
grid[i + k] = grid[i + k][:j] + 'o' + grid[i + k][j + 1:]
min_operations = min(min_operations, operations)

# Output the result
if min_operations == float('inf'):
print(-1)
else:
print(min_operations)
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
Meta-Llama-3.1-405B-Instruct-Turbo ```python
import sys

def solve():
H, W, K = map(int, sys.stdin.readline().split())
grid = [sys.stdin.readline().strip() for _ in range(H)]

def check_horizontal():
min_ops = float('inf')
for i in range(H):
ops = 0
left = 0
for j in range(W):
if grid[i][j] == 'x':
ops = 0
left = j + 1
elif grid[i][j] == '.':
ops += 1
if j - left + 1 >= K:
min_ops = min(min_ops, ops)
return min_ops

def check_vertical():
min_ops = float('inf')
for j in range(W):
ops = 0
top = 0
for i in range(H):
if grid[i][j] == 'x':
ops = 0
top = i + 1
elif grid[i][j] == '.':
ops += 1
if i - top + 1 >= K:
min_ops = min(min_ops, ops)
return min_ops

min_ops = min(check_horizontal(), check_vertical())
if min_ops == float('inf'):
print(-1)
else:
print(min_ops)

if __name__ == '__main__':
solve()
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
Meta-Llama-3.1-70B-Instruct-Turbo ```python
import sys

def main():
H, W, K = map(int, sys.stdin.readline().split())
S = [sys.stdin.readline().strip() for _ in range(H)]

def check(S):
min_ops = float('inf')
for i in range(H):
ops = 0
for j in range(W - K + 1):
for k in range(K):
if S[i][j + k] == '.':
ops += 1
if ops < min_ops:
min_ops = ops
ops -= S[i][j] == '.'
return min_ops

min_ops = min(check(S), check(list(zip(*S))))
if min_ops == float('inf'):
print(-1)
else:
print(min_ops)

if __name__ == '__main__':
main()
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
baichuan4 ```python
import sys

def min_operations(H, W, K, grid):
def check_consecutive(start_row, start_col, direction):
count = 0
for i in range(K):
if direction == 'horizontal':
if start_col + i >= W or grid[start_row][start_col + i] != 'o':
return -1
else: # vertical
if start_row + i >= H or grid[start_row + i][start_col] != 'o':
return -1
return 0

def dfs(row, col, operations):
if row == H:
return float('inf')
if col == W:
return dfs(row + 1, 0, operations)
if grid[row][col] == 'o':
return dfs(row, col + 1, operations)
if grid[row][col] == 'x':
return dfs(row, col + 1, operations)

# Try not to change the current cell
result = dfs(row, col + 1, operations)

# Change the current cell to 'o' and check for consecutive 'o's
grid[row][col] = 'o'
operations += 1
if check_consecutive(row, col, 'horizontal') == 0 or check_consecutive(row, col, 'vertical') == 0:
result = min(result, operations)
grid[row][col] = '.' # revert the change

return result

# Initialize the grid
grid = [list(line.strip()) for line in grid]

# Start DFS from the top-left corner
result = dfs(0, 0, 0)
return result if result != float('inf') else -1

# Read input from stdin
input_lines = [line.strip() for line in sys.stdin]
H, W, K = map(int, input_lines[0].split())
grid = input_lines[1:]

# Call the function and print the result
print(min_operations(H, W, K, grid))
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
doubao ```python
import math

H, W, K = map(int, input().split())
grid = [input() for _ in range(H)]

def count_ones(row, col, direction):
count = 0
for _ in range(K):
if direction == 'h' and col + _ < W and grid[row][col + _] == 'o':
count += 1
elif direction == 'v' and row + _ < H and grid[row + _][col] == 'o':
count += 1
return count

min_ops = math.inf
for i in range(H):
for j in range(W):
if grid[i][j] == '.':
grid[i] = grid[i][:j] + 'o' + grid[i][j + 1:]
h_count = max(count_ones(i, 0, 'h') for j in range(W - K + 1))
v_count = max(count_ones(0, j, 'v') for i in range(H - K + 1))
if h_count == K or v_count == K:
min_ops = min(min_ops, 1)
grid[i] = grid[i][:j] + '.' + grid[i][j + 1:]

if min_ops == math.inf:
print(-1)
else:
print(min_ops)
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
gpto1 ```python
# YOUR CODE HERE
import sys
import threading

def main():
import sys
import math
sys.setrecursionlimit(1<<25)
H, W, K = map(int, sys.stdin.readline().split())
S = [sys.stdin.readline().strip() for _ in range(H)]

min_ops = None
# Process horizontal sequences if K <= W
if K <= W:
for i in range(H):
A_row_x = [1 if c == 'x' else 0 for c in S[i]]
A_row_dot = [1 if c == '.' else 0 for c in S[i]]
prex_x = [0] * (W + 1)
prex_dot = [0] * (W + 1)
for j in range(W):
prex_x[j+1] = prex_x[j] + A_row_x[j]
prex_dot[j+1] = prex_dot[j] + A_row_dot[j]
for j in range(W - K + 1):
x_count = prex_x[j+K] - prex_x[j]
if x_count == 0:
dot_count = prex_dot[j+K] - prex_dot[j]
if min_ops is None or dot_count < min_ops:
min_ops = dot_count
# Process vertical sequences if K <= H
if K <= H:
for j in range(W):
A_col_x = [1 if S[i][j] == 'x' else 0 for i in range(H)]
A_col_dot = [1 if S[i][j] == '.' else 0 for i in range(H)]
prex_x = [0] * (H + 1)
prex_dot = [0] * (H + 1)
for i in range(H):
prex_x[i+1] = prex_x[i] + A_col_x[i]
prex_dot[i+1] = prex_dot[i] + A_col_dot[i]
for i in range(H - K + 1):
x_count = prex_x[i+K] - prex_x[i]
if x_count == 0:
dot_count = prex_dot[i+K] - prex_dot[i]
if min_ops is None or dot_count < min_ops:
min_ops = dot_count
if min_ops is None:
print(-1)
else:
print(min_ops)


if __name__ == '__main__':
threading.Thread(target=main).start()
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
kimi ```python
def main():
(H, W, K) = map(int, input().split())
S = [input() for _ in range(H)]
ans = float('inf')
for i in range(H):
cnt = 0
for j in range(W):
if S[i][j] == 'o':
cnt += 1
else:
cnt = 0
if cnt == K:
break
else:
cnt = 0
if cnt == K:
ans = 0
break
for j in range(W - K + 1):
cnt = 0
for k in range(K):
if S[i][j + k] == 'o':
cnt += 1
else:
break
ans = min(ans, K - cnt)
if ans == float('inf'):
ans = -1
print(ans if ans != float('inf') else min(ans, min((inf_row(S, K), inf_col(S, K)))))


def inf_row(S, K):
ans = float('inf')
for j in range(W):
cnt = 0
for i in range(H):
if S[i][j] == 'o':
cnt += 1
else:
cnt = 0
if cnt == K:
break
else:
cnt = 0
if cnt == K:
ans = 0
break
for i in range(H - K + 1):
cnt = 0
for k in range(K):
if S[i + k][j] == 'o':
cnt += 1
else:
break
ans = min(ans, K - cnt)
return ans


def inf_col(S, K):
ans = float('inf')
for i in range(H):
cnt = 0
for j in range(W):
if S[i][j] == 'o':
cnt += 1
else:
cnt = 0
if cnt == K:
break
else:
cnt = 0
if cnt == K:
ans = 0
break
for j in range(W - K + 1):
cnt = 0
for k in range(K):
if S[i][j + k] == 'o':
cnt += 1
else:
break
ans = min(ans, K - cnt)
return ans
main()
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
minimax ```python
# YOUR CODE HERE
from collections import deque

def min_operations(H, W, K, grid):
def count_o_in_line(line):
return line.count('o')

def can_form_sequence(line, K):
count = 0
for char in line:
if char == 'o':
count += 1
if count == K:
return True
else:
count = 0
return False

# Check for horizontal sequences
for line in grid:
if can_form_sequence(line, K):
return 0

# Check for vertical sequences
for col in range(W):
column = ''.join(grid[row][col] for row in range(H))
if can_form_sequence(column, K):
return 0

# Count the number of operations needed
operations = 0
for i in range(H):
for j in range(W):
if grid[i][j] == '.':
# Check the horizontal and vertical sequences that can be formed by changing this cell to 'o'
if (j <= W - K and all(grid[i][j+k] == '.' for k in range(K))) or \
(i <=		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
wenxinyiyan ```python
import sys

def min_operations(H, W, K, grid):
# Horizontal checks
min_ops = float('inf')
for i in range(H):
count_ops = 0
consecutive_os = 0
for j in range(W):
if grid[i][j] == 'o':
consecutive_os += 1
elif grid[i][j] == '.':
count_ops += 1
consecutive_os += 1
else:
consecutive_os = 0

if consecutive_os == K:
min_ops = min(min_ops, count_ops)
break

# Vertical checks
for j in range(W):
count_ops = 0
consecutive_os = 0
for i in range(H):
if grid[i][j] == 'o':
consecutive_os += 1
elif grid[i][j] == '.':
count_ops += 1
consecutive_os += 1
else:
consecutive_os = 0

if consecutive_os == K:
min_ops = min(min_ops, count_ops)
break

return min_ops if min_ops != float('inf') else -1

# Read input
H, W, K = map(int, sys.stdin.readline().split())
grid = []
for _ in range(H):
grid.append(sys.stdin.readline().strip())

# Solve and print result
result = min_operations(H, W, K, grid)
print(result)
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
zhipu ```python
def main():
import sys
input = sys.stdin.read
data = input().split()

H = int(data[0])
W = int(data[1])
K = int(data[2])
grid = data[3:]

# Initialize the minimum operations to a large number
min_operations = float('inf')

# Check horizontally
for i in range(H):
for j in range(W - K + 1):
count_dot = 0
valid = True
for k in range(K):
if grid[i][j + k] == 'x':
valid = False
break
if grid[i][j + k] == '.':
count_dot += 1
if valid:
min_operations = min(min_operations, count_dot)

# Check vertically
for j in range(W):
for i in range(H - K + 1):
count_dot = 0
valid = True
for k in range(K):
if grid[i + k][j] == 'x':
valid = False
break
if grid[i + k][j] == '.':
count_dot += 1
if valid:
min_operations = min(min_operations, count_dot)

# Output the result
if min_operations == float('inf'):
print(-1)
else:
print(min_operations)

if __name__ == "__main__":
main()
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]
deepseek-v3 ```python
# YOUR CODE HERE
H, W, K = map(int, input().split())
grid = [input().strip() for _ in range(H)]

min_ops = float('inf')

# Check horizontal sequences
for i in range(H):
for j in range(W - K + 1):
needed = 0
possible = True
for k in range(K):
if grid[i][j + k] == 'x':
possible = False
break
if grid[i][j + k] == '.':
needed += 1
if possible:
min_ops = min(min_ops, needed)

# Check vertical sequences
for j in range(W):
for i in range(H - K + 1):
needed = 0
possible = True
for k in range(K):
if grid[i + k][j] == 'x':
possible = False
break
if grid[i + k][j] == '.':
needed += 1
if possible:
min_ops = min(min_ops, needed)

if min_ops != float('inf'):
print(min_ops)
else:
print(-1)
```		 [{"input": "3 4 3\nxo.x\n..o.\nxx.o\n", "output": "2\n", "testtype": "stdin"}, {"input": "4 2 3\n.o\n.o\n.o\n.o\n", "output": "0\n", "testtype": "stdin"}, {"input": "3 3 3\nx..\n..x\n.x.\n", "output": "-1\n", "testtype": "stdin"}, {"input": "10 12 6\n......xo.o..\nx...x.....o.\nx...........\n..o...x.....\n.....oo.....\no.........x.\nox.oox.xx..x\n....o...oox.\n..o.....x.x.\n...o........\n", "output": "3\n", "testtype": "stdin"}]