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.IOException;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 29);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            CNuskeVsPhantomThnook solver = new CNuskeVsPhantomThnook();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class CNuskeVsPhantomThnook {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            int m = in.readInt();
            int q = in.readInt();
            //even for vertex, odd for edge
            int[][] mat = new int[n + 1][m + 1];
            //edge with top
            int[][] colEdge = new int[n + 1][m + 1];
            //edge with right
            int[][] rowEdge = new int[n + 1][m + 1];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    mat[i][j] = in.readChar() - '0';
                }
            }

            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    if (mat[i][j] + mat[i + 1][j] == 2) {
                        colEdge[i][j] = 1;
                    }
                    if (mat[i][j] + mat[i][j + 1] == 2) {
                        rowEdge[i][j] = 1;
                    }
                }
            }

            presum(mat);
            presum(colEdge);
            presum(rowEdge);

            for (int i = 0; i < q; i++) {
                int b = in.readInt() - 1;
                int l = in.readInt() - 1;
                int t = in.readInt() - 1;
                int r = in.readInt() - 1;

                int vertexCnt = region(mat, b, t, l, r);
                int edge = region(colEdge, b, t - 1, l, r) +
                        region(rowEdge, b, t, l, r - 1);

                int cc = vertexCnt - edge;
                out.println(cc);
            }
        }

        public int region(int[][] mat, int b, int t, int l, int r) {
            if (b > t || l > r) {
                return 0;
            }

            int ans = mat[t][r];
            if (b > 0) {
                ans -= mat[b - 1][r];
            }
            if (l > 0) {
                ans -= mat[t][l - 1];
            }
            if (b > 0 && l > 0) {
                ans += mat[b - 1][l - 1];
            }
            return ans;
        }

        public void presum(int[][] mat) {
            int n = mat.length;
            int m = mat[0].length;
            for (int i = 0; i < n; i++) {
                for (int j = 1; j < m; j++) {
                    mat[i][j] += mat[i][j - 1];
                }
                if (i > 0) {
                    for (int j = 0; j < m; j++) {
                        mat[i][j] += mat[i - 1][j];
                    }
                }
            }
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

        public char readChar() {
            skipBlank();
            char c = (char) next;
            next = read();
            return c;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(int c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(int c) {
            return append(c).println();
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }
}