You've got an n × m table (n rows and m columns), each cell of the table contains a "0" or a "1".

Your task is to calculate the number of rectangles with the sides that are parallel to the sides of the table and go along the cell borders, such that the number one occurs exactly k times in the rectangle. 

Input

The first line contains three space-separated integers n, m and k (1 ≤ n, m ≤ 2500, 0 ≤ k ≤ 6) — the sizes of the table and the required number of numbers one.

Next n lines each contains m characters "0" or "1". The i-th character of the j-th line corresponds to the character that is in the j-th row and the i-th column of the table.

Output

Print a single number — the number of rectangles that contain exactly k numbers one.

Please, do not write the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

3 3 2
101
000
101


Output

8


Input

5 5 1
00000
00000
00100
00000
00000


Output

81


Input

5 5 6
01010
10101
01010
10101
01010


Output

12


Input

3 3 0
001
010
000


Output

15


Input

4 4 0
0000
0101
0000
0000


Output

52
#include <bits/stdc++.h>
using namespace std;
inline char gc() {
  static char buf[100000], *p1 = buf, *p2 = buf;
  return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 100000, stdin), p1 == p2)
             ? EOF
             : *p1++;
}
inline int read() {
  char c = getchar();
  int tot = 1;
  while ((c < '0' || c > '9') && c != '-') c = getchar();
  if (c == '-') {
    tot = -1;
    c = getchar();
  }
  int sum = 0;
  while (c >= '0' && c <= '9') {
    sum = sum * 10 + c - '0';
    c = getchar();
  }
  return sum * tot;
}
inline void wr(long long x) {
  if (x < 0) {
    putchar('-');
    wr(-x);
    return;
  }
  if (x >= 10) wr(x / 10);
  putchar(x % 10 + '0');
}
inline void wrn(long long x) {
  wr(x);
  putchar('\n');
}
inline void wri(int x) {
  wr(x);
  putchar(' ');
}
inline void wrn(int x, int y) {
  wri(x);
  wrn(y);
}
inline void wrn(int a, int b, int c) {
  wri(a);
  wrn(b, c);
}
int n, m, K;
long long ans;
int s[3055][3055], up[8], down[8];
inline int sum(int x1, int x2, int y1, int y2) {
  return s[x2][y2] - s[x2][y1] - s[x1][y2] + s[x1][y1];
}
void work(int x1, int x2, int y1, int y2, bool dir) {
  if (x1 == x2 || y1 == y2) return;
  if ((x1 + 1 == x2) && (y1 + 1 == y2)) {
    ans += sum(x1, x2, y1, y2) == K;
    return;
  }
  if (dir) {
    int mid = ((x1 + x2) >> 1);
    work(x1, mid, y1, y2, !dir);
    work(mid, x2, y1, y2, !dir);
    for (int i = y1; i < y2; i++) {
      up[0] = down[0] = mid;
      for (int k = 1; k <= K + 1; k++) up[k] = x1, down[k] = x2;
      for (int j = i + 1; j <= y2; j++) {
        for (int k = 1; k <= K + 1; k++)
          while (sum(up[k], mid, i, j) >= k) up[k]++;
        for (int k = 1; k <= K + 1; k++)
          while (sum(mid, down[k], i, j) >= k) down[k]--;
        for (int k = 0; k <= K; k++)
          ans += (up[k] - up[k + 1]) * (down[K - k + 1] - down[K - k]);
      }
    }
  } else {
    int mid = ((y1 + y2) >> 1);
    work(x1, x2, y1, mid, !dir);
    work(x1, x2, mid, y2, !dir);
    for (int i = x1; i < x2; i++) {
      up[0] = down[0] = mid;
      for (int k = 1; k <= K + 1; k++) up[k] = y1, down[k] = y2;
      for (int j = i + 1; j <= x2; j++) {
        for (int k = 1; k <= K + 1; k++)
          while (sum(i, j, up[k], mid) >= k) up[k]++;
        for (int k = 1; k <= K + 1; k++)
          while (sum(i, j, mid, down[k]) >= k) down[k]--;
        for (int k = 0; k <= K; k++)
          ans += (up[k] - up[k + 1]) * (down[K - k + 1] - down[K - k]);
      }
    }
  }
}
char str[3055];
int main() {
  n = read();
  m = read();
  K = read();
  for (int i = (1); i <= (n); i++) {
    scanf("%s", str + 1);
    for (int j = (1); j <= (m); j++)
      s[i][j] = s[i - 1][j] + s[i][j - 1] - s[i - 1][j - 1] + str[j] - '0';
  }
  work(0, n, 0, m, 0);
  wrn(ans);
  return 0;
}
