蓝桥杯-统计子矩阵

"""
https://www.lanqiao.cn/problems/2109/learning/?page=1&first_category_id=1&name=%E7%BB%9F%E8%AE%A1%E5%AD%90%E7%9F%A9%E9%98%B5
"""
# 二维前缀和
# 利用前缀和思路只能通过70%
n, m, k = map(int, input().split())
# 下标从1开始
a = [[0] * (m + 1) for i in range(n + 1)]
sum = [[0] * (m + 1) for i in range(n + 1)]

# 输入一个二维数组
for i in range(1, n + 1):
  a[i] = [0] + list(map(int, input().split()))

# 求二维前缀和
for i in range(1, n + 1):
  for j in range(1, m + 1):
    sum[i][j] = sum[i - 1][j] + sum[i][j - 1] - sum[i - 1][j - 1] + a[i][j]

# 求二维区间前缀和
def get_sum(sum, x1, y1, x2, y2):
  return sum[x2][y2] - sum[x1 - 1][y2] - sum[x2][y1 - 1] + sum[x1 - 1][y1 - 1]

ans = 0
# 枚举矩阵左上角
for x1 in range(1, n + 1):
  for y1 in range(1, m + 1):
    # 枚举矩阵右下角
    for x2 in range(x1, n + 1):
      for y2 in range(y1, m + 1):
        if get_sum(sum, x1, y1, x2, y2) <= k:
          ans += 1
print(ans)