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.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Random;

public class Main {
	static ContestScanner in;
	static Writer out;
	public static void main(String[] args) {
		Main main = new Main();
		try {
			in = new ContestScanner();
			out = new Writer();
			main.solve();
			out.close();
			in.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}
	
	void solve() throws IOException {
		int n = in.nextInt();
		int m = in.nextInt();
		int q = in.nextInt();
		int[][] map = new int[n][m];
		for(int i = 0; i<n; i++) {
			char[] s = in.nextToken().toCharArray();
			for(int j = 0; j < m; j++) {
				map[i][j] = s[j] - '0';
			}
		}
		int[][] hor = new int[n][m];
		int[][] vir = new int[n][m];
		for(int i = 0; i<n; i++) {
			for(int j = 0; j < m - 1; j++) {
				if(map[i][j] == 1 && map[i][j+1] == 1) hor[i][j] = 1;
			}
		}
		for(int j = 0; j < m; j++) {
			for(int i = 0; i < n - 1; i++) {
				if(map[i][j] == 1 && map[i + 1][j] == 1) vir[i][j] = 1;
			}
		}
		makeSum(map);
		makeSum(hor);
		makeSum(vir);
		for(int Q = 0; Q < q; Q++) {
			int t = in.nextInt() -1;
			int l = in.nextInt() -1;
			int b = in.nextInt() -1;
			int r = in.nextInt() -1;
			int all = sum(map, l, r, t, b);
			int mHor = sum(hor, l, r - 1, t, b);
			int mVir = sum(vir, l, r, t, b - 1);
			out.println(all - mHor - mVir);
		}
	}
	
	int[][] makeSum(int[][] res) {
		int h = res.length;
		int w = res[0].length;
		for(int i = 0; i < h; i++) {
			for(int j = 1; j < w; j++) {
				res[i][j] += res[i][j-1];
			}
		}
		
		for(int j = 0; j < w; j++) {
			for(int i = 1; i < h; i++) {
				res[i][j] += res[i-1][j];
			}
		}
		return res;
	}
	
	int sum(int[][] imos, int l, int r, int t, int b) {
		if(l > r || t > b) return 0;
		int plus = 0;
		int minus = 0;
		if(l > 0 && t > 0) {
			plus += imos[t-1][l-1];
		}
		if(l > 0) {
			minus += imos[b][l-1];
		}
		if(t > 0) {
			minus += imos[t-1][r];
		}
		return imos[b][r] - minus + plus;
	}
}

class Writer extends PrintWriter{
	public Writer(String filename)throws IOException
	{super(new BufferedWriter(new FileWriter(filename)));}
	public Writer()throws IOException{super(System.out);}
}
class ContestScanner implements Closeable{
	private BufferedReader in;private int c=-2;
	public ContestScanner()throws IOException 
	{in=new BufferedReader(new InputStreamReader(System.in));}
	public ContestScanner(String filename)throws IOException
	{in=new BufferedReader(new InputStreamReader(new FileInputStream(filename)));}
	public String nextToken()throws IOException {
		StringBuilder sb=new StringBuilder();
		while((c=in.read())!=-1&&Character.isWhitespace(c));
		while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public String readLine()throws IOException{
		StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
		while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public long nextLong()throws IOException,NumberFormatException
	{return Long.parseLong(nextToken());}
	public int nextInt()throws NumberFormatException,IOException
	{return(int)nextLong();}
	public double nextDouble()throws NumberFormatException,IOException 
	{return Double.parseDouble(nextToken());}
	public void close() throws IOException {in.close();}
}