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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Text;
using CompLib.Util;

public class Program
{
    private int N, M, Q;
    private char[][] S;

    public void Solve()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        M = sc.NextInt();
        Q = sc.NextInt();
        S = new char[N][];
        for (int i = 0; i < N; i++)
        {
            S[i] = sc.NextCharArray();
        }

        /*
         * 範囲内の青マスの数 - 青マス同士の連結箇所
         */

        int[] sum = new int[(N + 1) * (M + 1)];
        {
            var line = new int[M + 1];
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < M; j++)
                {
                    line[j + 1] = line[j] + S[i][j] - '0';
                    sum[Conv(i + 1, j + 1)] = sum[Conv(i, j + 1)] + line[j + 1];
                }
            }
        }

        int[] yoko = new int[(N + 1) * M];
        {
            var line = new int[M];
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < M - 1; j++)
                {
                    line[j + 1] = line[j] + (S[i][j] == '1' && S[i][j + 1] == '1' ? 1 : 0);
                    yoko[ConvYoko(i + 1, j + 1)] = yoko[ConvYoko(i, j + 1)] + line[j + 1];
                }
            }
        }

        int[] tate = new int[N * (M + 1)];
        {
            var line = new int[M + 1];
            for (int i = 0; i < N - 1; i++)
            {
                for (int j = 0; j < M; j++)
                {
                    line[j + 1] = line[j] + (S[i][j] == '1' && S[i + 1][j] == '1' ? 1 : 0);
                    tate[ConvTate(i + 1, j + 1)] = tate[ConvTate(i, j + 1)] + line[j + 1];
                }
            }
        }

        var sb = new StringBuilder();
        for (int i = 0; i < Q; i++)
        {
            int x1 = sc.NextInt() - 1;
            int y1 = sc.NextInt() - 1;
            int x2 = sc.NextInt() - 1;
            int y2 = sc.NextInt() - 1;
            // 範囲内の青マス
            int cnt = sum[Conv(x2 + 1, y2 + 1)] - sum[Conv(x1, y2 + 1)] - sum[Conv(x2 + 1, y1)] + sum[Conv(x1, y1)];
            // 縦方向連結
            int t = tate[ConvTate(x2, y2 + 1)] - tate[ConvTate(x2, y1)] - tate[ConvTate(x1, y2 + 1)] +
                    tate[ConvTate(x1, y1)];
            // 横
            int y = yoko[ConvYoko(x2 + 1, y2)] - yoko[ConvYoko(x2 + 1, y1)] - yoko[ConvYoko(x1, y2)] +
                    yoko[ConvYoko(x1, y1)];
            sb.AppendLine((cnt - t - y).ToString());
        }

        Console.Write(sb.ToString());
    }

    private int ConvTate(int x, int y) => x * (M + 1) + y;
    private int ConvYoko(int x, int y) => x * M + y;
    private int Conv(int x, int y) => x * (M + 1) + y;

    public static void Main(string[] args) => new Program().Solve();
}

namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}