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.*;
import java.util.Arrays;
import java.util.StringJoiner;
import java.util.StringTokenizer;
import java.util.function.Function;

public class Main {

    static int H, W, Q;
    static char[][] S;
    static int[] H1, W1, H2, W2;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        H = sc.nextInt();
        W = sc.nextInt();
        Q = sc.nextInt();
        S = new char[H][];
        for (int i = 0; i < H; i++) {
            S[i] = sc.next().toCharArray();
        }
        H1 = new int[Q];
        W1 = new int[Q];
        H2 = new int[Q];
        W2 = new int[Q];
        for (int i = 0; i < Q; i++) {
            H1[i] = sc.nextInt()-1;
            W1[i] = sc.nextInt()-1;
            H2[i] = sc.nextInt()-1;
            W2[i] = sc.nextInt()-1;
        }

        writeLines(solve());
    }

    static int[] solve() {

        long[][] node = new long[H][W];
        for (int i = 0; i < H; i++) {
            for (int j = 0; j < W; j++) {
                node[i][j] = S[i][j] == '0' ? 0 : 1;
            }
        }

        long[][] edge1 = new long[H][W-1];
        for (int h = 0; h < H; h++) {
            for (int w = 0; w < W-1; w++) {
                if( S[h][w] == '1' && S[h][w+1] == '1') {
                    edge1[h][w] = 1;
                }
            }
        }
        long[][] edge2 = new long[H-1][W];
        for (int w = 0; w < W; w++) {
            for (int h = 0; h < H-1; h++) {
                if( S[h][w] == '1' && S[h+1][w] == '1') {
                    edge2[h][w] = 1;
                }
            }
        }

        CumulativeSum2D node_2d = new CumulativeSum2D();
        node_2d.init(H, W, node);
        CumulativeSum2D edge1_2d = new CumulativeSum2D();
        edge1_2d.init(H, W-1, edge1);
        CumulativeSum2D edge2_2d = new CumulativeSum2D();
        edge2_2d.init(H-1, W, edge2);

        int[] ans = new int[Q];
        for (int i = 0; i < Q; i++) {
            int n = (int)node_2d.get(H1[i], W1[i], H2[i], W2[i]);
            int e1;
            if( W1[i] != W2[i] ) {
                e1 = (int)edge1_2d.get(H1[i], W1[i], H2[i], W2[i]-1);
            } else {
                e1 = 0;
            }
            int e2;
            if( H1[i] != H2[i] ) {
                e2 = (int)edge2_2d.get(H1[i], W1[i], H2[i]-1, W2[i]);
            } else {
                e2 = 0;
            }
            ans[i] = n - e1 - e2;
        }

        return ans;
    }

    static class CumulativeSum2D {

        long[][] cs2d;

        void init(int h, int w, long[][] c) {
            this.cs2d = c;
            for (int i = 0; i < h; i++) {
                for (int j = 1; j < w; j++) {
                    c[i][j] += c[i][j-1];
                }
            }
            for (int j = 0; j < w; j++) {
                for (int i = 1; i < h; i++) {
                    c[i][j] += c[i-1][j];
                }
            }
        }

        // 左上が (h1, w1), 左下が(h2, w2), 閉区間
        long get(int h1, int w1, int h2, int w2) {
            // d c
            // b a
            long abcd = cs2d[h2][w2];

            long cd;
            if( h1 > 0 ) {
                cd = cs2d[h1-1][w2];
            } else {
                cd = 0;
            }

            long bd;
            if( w1 > 0 ) {
                bd = cs2d[h2][w1-1];
            } else {
                bd = 0;
            }

            long d;
            if( w1 > 0 && h1 > 0 ) {
                d = cs2d[h1-1][w1-1];
            } else {
                d = 0;
            }

            return abcd - cd - bd + d;
        }
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

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

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt() + delta;
            return a;
        }

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

    static <A> void writeLines(A[] as, Function<A, String> f) {
        PrintWriter pw = new PrintWriter(System.out);
        for (A a : as) {
            pw.println(f.apply(a));
        }
        pw.flush();
    }

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg.toString());
        }
        System.err.println(j.toString());
    }
}