Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

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

Sample Output 1

3
2
2
2

In the first query, the whole grid is specified. There are three components consisting of blue squares, and thus 3 should be printed.

In the second query, the region within the red frame is specified. There are two components consisting of blue squares, and thus 2 should be printed.
Note that squares that belong to the same component in the original grid may belong to different components.

Sample Input 2

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

Sample Output 2

3
2
1
1
3
2

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Memory Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.NoSuchElementException;

public class Main {

  private void solve(FastScanner in, PrintWriter out) {
    int N = in.nextInt();
    int M = in.nextInt();
    int Q = in.nextInt();
    long[][] map = new long[N][M];
    for (int i = 0; i < N; i++) {
      String S = in.next();
      for (int j = 0; j < M; j++) {
        map[i][j] = S.charAt(j) - '0';
      }
    }

    long[][] edgeV = new long[N][M];
    long[][] edgeH = new long[N][M];
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < M; j++) {
        if (j + 1 < M) {
          edgeH[i][j] = map[i][j] == 1 && map[i][j + 1] == 1 ? 1 : 0;
        }
        if (i > 0) {
          edgeV[i][j] = map[i][j] == 1 && map[i - 1][j] == 1 ? 1 : 0;
        }
      }
    }

    CumulativeSum sum = new CumulativeSum(map);
    CumulativeSum sumV = new CumulativeSum(edgeV);
    CumulativeSum sumH = new CumulativeSum(edgeH);
    for (int q = 0; q < Q; q++) {
      int i1 = in.nextInt() - 1;
      int j1 = in.nextInt() - 1;
      int i2 = in.nextInt() - 1;
      int j2 = in.nextInt() - 1;
      long ans = sum.getSum(i1, j1, i2, j2);
      ans -= sumV.getSum(i1 + 1, j1, i2, j2);
      ans -= sumH.getSum(i1, j1, i2, j2 - 1);
      out.println(ans);
    }

  }

  public class CumulativeSum {

    int nx, ny;
    long[][] sum;

    CumulativeSum(final long[][] a) {
      ny = a.length;
      nx = a[0].length;
      sum = new long[ny + 1][nx + 1];
      for (int i = 0; i < ny; i++) {
        for (int j = 0; j < nx; j++) {
          sum[i + 1][j + 1] = a[i][j] + sum[i][j + 1] + sum[i + 1][j] - sum[i][j];
        }
      }
    }

    long getSum(int y1, int x1, int y2, int x2) {
      if (y1 > y2 || x1 > x2) {
        return 0;
      }
      y1 = Math.max(y1, 0);
      x1 = Math.max(x1, 0);
      y2 = Math.min(y2, ny - 1);
      x2 = Math.min(x2, nx - 1);
      return sum[y2 + 1][x2 + 1] - sum[y1][x2 + 1] - sum[y2 + 1][x1] + sum[y1][x1];
    }
  }

  public static void main(String[] args) {
    PrintWriter out = new PrintWriter(System.out);
    new Main().solve(new FastScanner(), out);
    out.close();
  }

  private static class FastScanner {

    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int bufferLength = 0;

    private boolean hasNextByte() {
      if (ptr < bufferLength) {
        return true;
      } else {
        ptr = 0;
        try {
          bufferLength = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (bufferLength <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) {
        return buffer[ptr++];
      } else {
        return -1;
      }
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) {
        ptr++;
      }
    }

    boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) {
        throw new NoSuchElementException();
      }
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    public int loadChar(char[] buf) {
      if (!hasNext()) {
        throw new NoSuchElementException();
      }
      int pos = 0;
      int b = readByte();
      while (isPrintableChar(b)) {
        buf[pos] = (char) b;
        b = readByte();
        pos++;
      }
      return pos;
    }

    long nextLong() {
      if (!hasNext()) {
        throw new NoSuchElementException();
      }
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    double[] nextDoubleArray(int n) {
      double[] array = new double[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextDouble();
      }
      return array;
    }

    double[][] nextDoubleMap(int n, int m) {
      double[][] map = new double[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextDoubleArray(m);
      }
      return map;
    }

    public int nextInt() {
      return (int) nextLong();
    }

    public int[] nextIntArray(int n) {
      int[] array = new int[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextInt();
      }
      return array;
    }

    public long[] nextLongArray(int n) {
      long[] array = new long[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextLong();
      }
      return array;
    }

    public String[] nextStringArray(int n) {
      String[] array = new String[n];
      for (int i = 0; i < n; i++) {
        array[i] = next();
      }
      return array;
    }

    public char[][] nextCharMap(int n) {
      char[][] array = new char[n][];
      for (int i = 0; i < n; i++) {
        array[i] = next().toCharArray();
      }
      return array;
    }

    public int[][] nextIntMap(int n, int m) {
      int[][] map = new int[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextIntArray(m);
      }
      return map;
    }
  }
}