Problem: Nuske has a grid with N rows and M columns of squares. The rows are numbered 1 through N from top to bottom, and the columns are numbered 1 through M from left to right. Each square in the grid is painted in either blue or white. If S_{i,j} is 1, the square at the i-th row and j-th column is blue; if S_{i,j} is 0, the square is white. For every pair of two blue square a and b, there is at most one path that starts from a, repeatedly proceeds to an adjacent (side by side) blue square and finally reaches b, without traversing the same square more than once.

Phantom Thnook, Nuske's eternal rival, gives Q queries to Nuske. The i-th query consists of four integers x_{i,1}, y_{i,1}, x_{i,2} and y_{i,2} and asks him the following: when the rectangular region of the grid bounded by (and including) the x_{i,1}-th row, x_{i,2}-th row, y_{i,1}-th column and y_{i,2}-th column is cut out, how many connected components consisting of blue squares there are in the region?

Process all the queries.

Constraints

* 1 ≤ N,M ≤ 2000
* 1 ≤ Q ≤ 200000
* S_{i,j} is either 0 or 1.
* S_{i,j} satisfies the condition explained in the statement.
* 1 ≤ x_{i,1} ≤ x_{i,2} ≤ N(1 ≤ i ≤ Q)
* 1 ≤ y_{i,1} ≤ y_{i,2} ≤ M(1 ≤ i ≤ Q)

Input

The input is given from Standard Input in the following format:


N M Q
S_{1,1}..S_{1,M}
:
S_{N,1}..S_{N,M}
x_{1,1} y_{i,1} x_{i,2} y_{i,2}
:
x_{Q,1} y_{Q,1} x_{Q,2} y_{Q,2}


Output

For each query, print the number of the connected components consisting of blue squares in the region.

Examples

Input

3 4 4
1101
0110
1101
1 1 3 4
1 1 3 1
2 2 3 4
1 2 2 4


Output

3
2
2
2


Input

5 5 6
11010
01110
10101
11101
01010
1 1 5 5
1 2 4 5
2 3 3 4
3 3 3 3
3 1 3 5
1 1 3 4


Output

3
2
1
1
3
2

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author ilyakor
 */
public class Main {

  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    OutputWriter out = new OutputWriter(outputStream);
    TaskC solver = new TaskC();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskC {

    char[][] a;

    public void solve(int testNumber, InputReader in, OutputWriter out) {
      int n = in.nextInt();
      int m = in.nextInt();
      int q = in.nextInt();
      a = new char[n][];
      for (int i = 0; i < n; ++i) {
        a[i] = in.nextToken().toCharArray();
      }
      int[][] s1 = new int[n + 1][m + 1];
      int[][] s2 = new int[n + 1][m + 1];
      int[][] s3 = new int[n + 1][m + 1];
      for (int i = 0; i < n; ++i) {
        for (int j = 0; j < m; ++j) {
          if (a[i][j] == '0') {
            continue;
          }
          s1[i + 1][j + 1] = 1;
          if (i + 1 < n && a[i + 1][j] == '1') {
            ++s2[i + 1][j + 1];
          }
          if (j + 1 < m && a[i][j + 1] == '1') {
            ++s3[i + 1][j + 1];
          }
        }
      }
      for (int i = 0; i < n; ++i) {
        for (int j = 1; j < m; ++j) {
          s1[i + 1][j + 1] += s1[i + 1][j];
          s2[i + 1][j + 1] += s2[i + 1][j];
          s3[i + 1][j + 1] += s3[i + 1][j];
        }
      }
      for (int i = 1; i < n; ++i) {
        for (int j = 0; j < m; ++j) {
          s1[i + 1][j + 1] += s1[i][j + 1];
          s2[i + 1][j + 1] += s2[i][j + 1];
          s3[i + 1][j + 1] += s3[i][j + 1];
        }
      }

      for (int it = 0; it < q; ++it) {
        int x1 = in.nextInt() - 1;
        int y1 = in.nextInt() - 1;
        int x2 = in.nextInt() - 1;
        int y2 = in.nextInt() - 1;
        int V = s1[x2 + 1][y2 + 1] - s1[x1][y2 + 1] - s1[x2 + 1][y1] + s1[x1][y1];
        int E1 = s2[x2][y2 + 1] - s2[x1][y2 + 1] - s2[x2][y1] + s2[x1][y1];
        int E2 = s3[x2 + 1][y2] - s3[x1][y2] - s3[x2 + 1][y1] + s3[x1][y1];
        int res = V - E1 - E2;
        out.printLine(res);
      }
    }

  }

  static class OutputWriter {

    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
      writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
      this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
      for (int i = 0; i < objects.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(objects[i]);
      }
    }

    public void printLine(Object... objects) {
      print(objects);
      writer.println();
    }

    public void close() {
      writer.close();
    }

  }

  static class InputReader {

    private InputStream stream;
    private byte[] buffer = new byte[10000];
    private int cur;
    private int count;

    public InputReader(InputStream stream) {
      this.stream = stream;
    }

    public static boolean isSpace(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public int read() {
      if (count == -1) {
        throw new InputMismatchException();
      }
      try {
        if (cur >= count) {
          cur = 0;
          count = stream.read(buffer);
          if (count <= 0) {
            return -1;
          }
        }
      } catch (IOException e) {
        throw new InputMismatchException();
      }
      return buffer[cur++];
    }

    public int readSkipSpace() {
      int c;
      do {
        c = read();
      } while (isSpace(c));
      return c;
    }

    public String nextToken() {
      int c = readSkipSpace();
      StringBuilder sb = new StringBuilder();
      while (!isSpace(c)) {
        sb.append((char) c);
        c = read();
      }
      return sb.toString();
    }

    public int nextInt() {
      int sgn = 1;
      int c = readSkipSpace();
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      int res = 0;
      do {
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res = res * 10 + c - '0';
        c = read();
      } while (!isSpace(c));
      res *= sgn;
      return res;
    }

  }
}