A tourist wants to visit country Zeydabad for Zbazi (a local game in Zeydabad).

The country Zeydabad is a rectangular table consisting of n rows and m columns. Each cell on the country is either 'z' or '.'.

The tourist knows this country is named Zeydabad because there are lots of ''Z-pattern"s in the country. A ''Z-pattern" is a square which anti-diagonal is completely filled with 'z' and its upper and lower rows are also completely filled with 'z'. All other cells of a square can be arbitrary.

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Note that a ''Z-pattern" can consist of only one cell (see the examples).

So he wants to count the number of ''Z-pattern"s in the country (a necessary skill for Zbazi).

Now your task is to help tourist with counting number of ''Z-pattern"s.

As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use gets/scanf/printf instead of getline/cin/cout in C++, prefer to use BufferedReader/PrintWriter instead of Scanner/System.out in Java.

Input

The first line contains two integers n, m (1 ≤ n, m ≤ 3000) — the number of rows and columns respectively.

Each of the next n lines contains m characters 'z' or '.' — the description of Zeydabad.

Output

Print the only integer a — the number of ''Z-pattern"s in Zeydabad.

Examples

Input

4 4
zzzz
zzz.
.z..
zzzz


Output

16


Input

1 4
z.z.


Output

2


Input

2 2
zz
zz


Output

5
#include <bits/stdc++.h>
#pragma warning(disable : 4996)
using namespace std;
char buf[4000][4000];
int fw[3000][3000];
int bw[3000][3000];
int tmpfw[4000];
int tmpbw[4000];
const int B = 4096;
struct BIT {
  int tr[2 * B];
  BIT() {}
  void init() {
    for (int i = 0; i < 2 * B; i++) tr[i] = 0;
  }
  void upd(int i) {
    tr[B + i]++;
    int cur = (B + i) / 2;
    while (cur > 0) {
      tr[cur]++;
      cur /= 2;
    }
  }
  int get(int nd, int ndl, int ndr, int l, int r) {
    if (l > ndr || ndl > r)
      return 0;
    else if (l <= ndl && ndr <= r)
      return tr[nd];
    else {
      int mid = (ndl + ndr) / 2;
      return get(2 * nd, ndl, mid, l, r) + get(2 * nd + 1, mid + 1, ndr, l, r);
    }
  }
};
BIT bit;
int main() {
  int n, m;
  scanf("%d%d", &(n), &(m));
  for (int i = 0; i < n; i++) scanf("%s", buf[i]);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      if (buf[i][j] == '.') {
      } else if (j == 0)
        fw[i][j] = 1;
      else
        fw[i][j] = fw[i][j - 1] + 1;
      if (buf[i][m - 1 - j] == '.') {
      } else if (j == 0)
        bw[i][m - 1 - j] = 1;
      else
        bw[i][m - 1 - j] = bw[i][m - j] + 1;
    }
  }
  long long ans = 0;
  for (int sum = 0; sum < m + n - 1; sum++) {
    int s, e;
    if (sum < n) {
      s = 0;
    } else
      s = sum - n + 1;
    if (sum < m)
      e = sum;
    else {
      e = m - 1;
    }
    int cur = -1;
    for (int i = s; i <= e; i++) {
      if (buf[sum - i][i] == '.') {
        cur = -1;
      } else {
        if (cur == -1) cur = i;
        tmpbw[i] = cur;
      }
    }
    cur = -1;
    for (int i = e; i >= s; i--) {
      if (buf[sum - i][i] == '.') {
        cur = -1;
      } else {
        if (cur == -1) cur = i;
        tmpfw[i] = cur;
      }
    }
    vector<pair<int, int> > fi;
    vector<pair<int, int> > se;
    for (int i = s; i <= e; i++) {
      if (buf[sum - i][i] == '.') continue;
      int power = i + bw[sum - i][i] - 1;
      power = min(power, tmpfw[i]);
      fi.push_back(make_pair(i, power));
    }
    for (int i = s; i <= e; i++) {
      if (buf[sum - i][i] == '.') continue;
      int power = i - fw[sum - i][i] + 1;
      power = max(power, tmpbw[i]);
      se.push_back(make_pair(power, i));
    }
    sort(fi.begin(), fi.end());
    sort(se.begin(), se.end());
    auto it = fi.begin();
    auto it2 = se.begin();
    bit.init();
    for (int i = s; i <= e; i++) {
      for (; it2 != se.end(); it2++) {
        if (it2->first != i)
          break;
        else {
          bit.upd(it2->second - s);
        }
      }
      for (; it != fi.end(); it++) {
        if (it->first != i)
          break;
        else {
          ans += bit.get(1, 0, B - 1, it->first - s, it->second - s);
        }
      }
    }
  }
  printf("%I64d", ans);
  return 0;
}
