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.Collections.Generic;
using System.Linq;
using System.IO;
using System.Runtime.CompilerServices;
using System.Text;
using static Template;

namespace SolveSpace
{
    using static System.Console;
    using static System.Convert;
    using static System.Math;
    using Pi = Pair<int, int>;
    using Number = System.Int64;

    class Solver
    {
        public void Solve()
        {
            int n, m, q;
            Input.Make(out n, out m, out q);

            var gred = Enumerable.Repeat(0, n).Select(_ => new int[m]).ToArray();
            for (var i = 0; i < n; i++)
            {
                var s = ReadLine();
                for (var j = 0; j < m; j++)
                    gred[i][j] = s[j] - '0';
            }
            var vexsum = new BIT2D(n + 1, m + 1);
            for (var i = 1; i <= n; i++)
                for (var j = 1; j <= m; j++)
                    if (gred[i - 1][j - 1] == 1)
                        vexsum.Add(i, j, 1);
            var xsum = new BIT2D(n + 1, m + 1);
            var ysum = new BIT2D(n + 1, m + 1);
            for (var i = 1; i <= n; i++)
                for (var j = 1; j <= m; j++)
                    if (gred[i - 1][j - 1] == 1)
                    {
                        if (i != 1 && gred[i - 2][j - 1] == 1)
                            xsum.Add(i, j, 1);
                        if (j != 1 && gred[i - 1][j - 2] == 1)
                            ysum.Add(i, j, 1);
                    }
            for (var i = 0; i < q; i++)
            {
                int x1, y1, x2, y2;
                Input.Make(out x1, out y1, out x2, out y2);
                var v = vexsum.RangeSum(x1, y1, x2, y2);
                var e = 0L;
                if (x1 != x2)
                    e += xsum.RangeSum(x1 + 1, y1, x2, y2);
                if (y1 != y2)
                    e += ysum.RangeSum(x1, y1 + 1, x2, y2);
                WriteLine(v - e);
            }
        }
    }
    class BIT2D
    {
        int H, W;
        Number[] item;
        public Number this[int i,int j]
        {
            get { return RangeSum(i, j, i, j); }
            set { Add(i, j, value - this[i, j]); }
        }
        public BIT2D(int h, int w)
        { H = h; W = w; item = new Number[h * w]; }
        public void Add(int h,int w,Number val)
        { for (++h; h <= H; h += h & -h) AddX(h, w, val); }
        public void AddRange(int h1,int w1,int h2,int w2,Number val)
        {
            Add(h1, w1, val);
            if (h2 + 1 < H) Add(h2 + 1, w1, -val);
            if (w2 + 1 < W) Add(h1, w2 + 1, -val);
            if (h2 + 1 < H && w2 + 1 < W) Add(h2 + 1, w2 + 1, val);
        }
        public Number Sum(int h,int w)
        {
            Number r = 0;
            for (++h; h > 0; h -= h & -h) r += SumX(h, w);
            return r;
        }
        public Number RangeSum(int h1, int w1, int h2, int w2)
            => Sum(h2, w2) - Sum(h1 - 1, w2) - Sum(h2, w1 - 1) + Sum(h1 - 1, w1 - 1);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        private int id(int h, int w) => (h - 1) * W + w - 1;
        private void AddX(int h, int w, Number val)
        { for (++w; w <= W; w += w & -w) item[id(h, w)] += val; }
        private Number SumX(int h,int w)
        {
            Number r = 0;
            for (++w; w > 0; w -= w & -w) r += item[id(h, w)];
            return r;
        }
    }
}

#region Template
public class Template
{
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmin<T>(ref T num, T val) where T : IComparable<T>
    { if (num.CompareTo(val) == 1) { num = val; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmax<T>(ref T num, T val) where T : IComparable<T>
    { if (num.CompareTo(val) == -1) { num = val; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(ref T v1, ref T v2)
    { var t = v2; v2 = v1; v1 = t; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static T[] Create<T>(int n, Func<T> f)
        => Enumerable.Repeat(0, n).Select(_ => f()).ToArray();
    public static void Fail() => Fail("No");
    public static void Fail<T>(T s) { Console.WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        var p = new SolveSpace.Solver();
        for (var i = 1; i > 0; --i)
            p.Solve();
        Console.Out.Flush();
    }
}

public class Input
{
    public static string read => Console.ReadLine().Trim();
    public static int[] ar => read.Split(' ').Select(int.Parse).ToArray();
    public static int num => Convert.ToInt32(read);
    public static long[] arL => read.Split(' ').Select(long.Parse).ToArray();
    public static long numL => Convert.ToInt64(read);
    public static char[][] grid(int h)
        => Create(h, () => read.ToCharArray());
    public static int[] ar1D(int n)
        => Create(n, () => num);
    public static long[] arL1D(int n)
        => Create(n, () => numL);
    public static string[] strs(int n)
        => Create(n, () => read);
    public static int[][] ar2D(int n)
        => Create(n, () => ar);
    public static long[][] arL2D(int n)
        => Create(n, () => arL);
    public static List<T>[] edge<T>(int n)
        => Create(n, () => new List<T>());
    public static void Make<T1, T2>(out T1 v1, out T2 v2)
    {
        v1 = Next<T1>();
        v2 = Next<T2>();
    }
    public static void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3)
    {
        Make(out v1, out v2);
        v3 = Next<T3>();
    }
    public static void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4)
    {
        Make(out v1, out v2, out v3);
        v4 = Next<T4>();
    }
    public static void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5)
    {
        Make(out v1, out v2, out v3, out v4);
        v5 = Next<T5>();
    }
    public static void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6)
    {
        Make(out v1, out v2, out v3, out v4, out v5);
        v6 = Next<T6>();
    }
    static Input()
    {
        sc = new Queue<string>();
        dic = new Dictionary<Type, Func<string, object>>();
        dic[typeof(int)] = s => int.Parse(s);
        dic[typeof(long)] = s => long.Parse(s);
        dic[typeof(char)] = s => char.Parse(s);
        dic[typeof(double)] = s => double.Parse(s);
        dic[typeof(uint)] = s => uint.Parse(s);
        dic[typeof(ulong)] = s => ulong.Parse(s);
        dic[typeof(string)] = s => s;
    }
    private static Dictionary<Type, Func<string, object>> dic;
    private static Queue<string> sc;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static T Next<T>() { if (sc.Count == 0) foreach (var item in read.Split(' ')) sc.Enqueue(item); return (T)dic[typeof(T)](sc.Dequeue()); }
    public const int MOD = 1000000007;
}

public class Pair<T1, T2> : IComparable<Pair<T1, T2>>
{
    public T1 v1;
    public T2 v2;
    public Pair() { v1 = Input.Next<T1>(); v2 = Input.Next<T2>(); }
    public Pair(T1 v1, T2 v2)
    { this.v1 = v1; this.v2 = v2; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int CompareTo(Pair<T1, T2> p)
    {
        var c = Comparer<T1>.Default.Compare(v1, p.v1);
        if (c == 0)
            c = Comparer<T2>.Default.Compare(v2, p.v2);
        return c;
    }
    public override string ToString()
        => $"{v1.ToString()} {v2.ToString()}";
}

public class Pair<T1, T2, T3> : Pair<T1, T2>, IComparable<Pair<T1, T2, T3>>
{
    public T3 v3;
    public Pair() : base() { v3 = Input.Next<T3>(); }
    public Pair(T1 v1, T2 v2, T3 v3) : base(v1, v2)
    { this.v3 = v3; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int CompareTo(Pair<T1, T2, T3> p)
    {
        var c = base.CompareTo(p);
        if (c == 0)
            c = Comparer<T3>.Default.Compare(v3, p.v3);
        return c;
    }
    public override string ToString()
        => $"{base.ToString()} {v3.ToString()}";
}
#endregion