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


public class Main {
  public static void main(String[] args) {
    FastScanner sc = new FastScanner();
    int N = sc.nextInt();
    int M = sc.nextInt();
    int Q = sc.nextInt();
    
    int[][] map = new int[N + 2][M + 2];
    for (int i = 1; i <= N; i ++) {
      char[] s = sc.next().toCharArray();
      for (int j = 1; j <= M; j ++) {
        map[i][j] = s[j - 1] - '0';
      }
    }
    
    int[][] e = new int[N + 2][M + 2];
    int[][] v = new int[N + 2][M + 2];

    int[][] dir = {{-1, 0}, {0, -1}};
    for (int i = 1; i <= N; i ++) {
      for (int j = 1; j <= M; j ++) {
        v[i][j] = v[i][j - 1];
        e[i][j] = e[i][j - 1];
        if (map[i][j] == 1) {
          v[i][j] ++;
          
          for (int[] d : dir) {
            if (map[i + d[0]][j + d[1]] == 1) {
              e[i][j] ++;
            }
          }
        }
      }
      for (int j = 1; j <= M; j ++) {
        v[i][j] += v[i - 1][j];
        e[i][j] += e[i - 1][j];
      }
    }
    
    int[][][] ex = new int[2][N + 1][M + 1];
    for (int i = 1; i <= N; i ++) {
      for (int j = 1; j <= M; j ++) {
        ex[0][i][j] = ex[0][i][j - 1];
        if (map[i][j] == 1 && map[i - 1][j] == 1) {
          ex[0][i][j] ++;
        }
      }
    }
    for (int j = 1; j <= M; j ++) {
      for (int i = 1; i <= N; i ++) {
        ex[1][i][j] = ex[1][i - 1][j];
        if (map[i][j] == 1 && map[i][j - 1] == 1) {
          ex[1][i][j] ++;
        }
      }
    }
    
    StringBuilder sb = new StringBuilder();
    for (int i = 0; i < Q; i ++) {
      int x1 = sc.nextInt();
      int y1 = sc.nextInt();
      int x2 = sc.nextInt();
      int y2 = sc.nextInt();
      
      int v1 = v[x2][y2] - v[x1 - 1][y2] - v[x2][y1 - 1] + v[x1 - 1][y1 - 1];
      int e1 = e[x2][y2] - e[x1 - 1][y2] - e[x2][y1 - 1] + e[x1 - 1][y1 - 1];
      
      int et = ex[0][x1][y2] - ex[0][x1][y1 - 1];
      int el = ex[1][x2][y1] - ex[1][x1 - 1][y1];

      
      sb.append(v1 - (e1 - et - el));
      sb.append("\n");
    }
    System.out.println(sb);
  }

}


class FastScanner {
	public static String debug = null;

	private final InputStream in = System.in;
	private int ptr = 0;
	private int buflen = 0;
	private byte[] buffer = new byte[1024];
	private boolean eos = false;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				if (debug != null) {
					buflen = debug.length();
					buffer = debug.getBytes();
					debug = "";
					eos = true;
				} else {
					buflen = in.read(buffer);
				}
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen < 0) {
				eos = true;
				return false;
			} else if (buflen == 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++;
	}

	public boolean isEOS() {
		return this.eos;
	}

	public 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 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();
		}
	}

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

	public long[] nextLongList(int n) {
		return nextLongTable(1, n)[0];
	}

	public int[] nextIntList(int n) {
		return nextIntTable(1, n)[0];
	}

	public long[][] nextLongTable(int n, int m) {
		long[][] ret = new long[n][m];
		for (int i = 0; i < n; i ++) {
			for (int j = 0; j < m; j ++) {
				ret[i][j] = nextLong();
			}
		}
		return ret;
	}

	public int[][] nextIntTable(int n, int m) {
		int[][] ret = new int[n][m];
		for (int i = 0; i < n; i ++) {
			for (int j = 0; j < m; j ++) {
				ret[i][j] = nextInt();
			}
		}
		return ret;
	}
}