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.math.*;
import java.util.*;

import static java.util.Arrays.*;

public class Main {
	private static final int mod = (int)1e9+7;

	final Random random = new Random(0);
	final IOFast io = new IOFast();

	/// MAIN CODE
	public void run() throws IOException {
//		int TEST_CASE = Integer.parseInt(new String(io.nextLine()).trim());
		int TEST_CASE = 1;
		while(TEST_CASE-- != 0) {
			int h = io.nextInt();
			int w = io.nextInt();
			int q = io.nextInt();
			char[][] cs = new char[h][];
			int[][] deg = new int[h][w];
			for (int y = 0; y < h; y++) {
				cs[y] = io.next();
				for (int x = 0; x < w; x++) {
					if (cs[y][x] == '1') {
						if (x > 0 && cs[y][x-1] == '1') { deg[y][x]++; deg[y][x-1]++; }
						if (y > 0 && cs[y-1][x] == '1') { deg[y][x]++; deg[y-1][x]++; }
					}
				}
			}
			
			int[] d = new int[]{1,0,-1,0,1};
			int[] st = new int[w * h * 2 + 100];
			boolean[][] vis = new boolean[h][w];
			int[][] inc = new int[h+1][w+1];
			int[][] incx0 = new int[h+1][w+1];
			int[][] incx1 = new int[h+1][w+1];
			int[][] incy0 = new int[h+1][w+1];
			int[][] incy1 = new int[h+1][w+1];
			for (int y = 0; y < h; y++) {
				for (int x = 0; x < w; x++) if (cs[y][x] == '1' && deg[y][x] <= 1 && !vis[y][x]) {
					vis[y][x] = true;
					int sp = 0;
					st[sp++] = y<<16|x;
					inc[y+1][x+1]++;
					while (sp > 0) {
						int xx = st[--sp] & 0xFFFF;
						int yy = st[sp] >> 16;
						for (int i = 0; i < 4; i++) {
							int x2 = xx + d[i], y2 = yy + d[i+1];
							if (x2 < 0 || y2 < 0 || x2 >= w || y2 >= h || vis[y2][x2] || cs[y2][x2] == '0') continue;
							vis[y2][x2] = true;
							st[sp++] = y2<<16|x2;
							if (xx < x2) incx1[y2+1][x2+1]++;
							if (xx > x2) incx0[y2+1][x2+1]++;
							if (yy < y2) incy1[y2+1][x2+1]++;
							if (yy > y2) incy0[y2+1][x2+1]++;
						}
					}
				}
			}
			
			for (int x = 0; x <= w; x++) {
				for (int y = 1; y <= h; y++) {
					incx0[y][x] += incx0[y-1][x];
					incx1[y][x] += incx1[y-1][x];
					incy0[y][x] += incy0[y-1][x];
					incy1[y][x] += incy1[y-1][x];
					inc[y][x] += inc[y-1][x];
				}
			}
			for (int y = 0; y <= h; y++) {
				for (int x = 1; x <= w; x++) {
					incx0[y][x] += incx0[y][x-1];
					incx1[y][x] += incx1[y][x-1];
					incy0[y][x] += incy0[y][x-1];
					incy1[y][x] += incy1[y][x-1];
					inc[y][x] += inc[y][x-1];
				}
			}
			
			while (q-- > 0) {
				int y0 = io.nextInt();
				int x0 = io.nextInt();
				int y1 = io.nextInt();
				int x1 = io.nextInt();
				int ans = sum(inc, x1, y1, x0 - 1, y0 - 1);
				ans += sum(incx1, x0-0, y1, x0-1, y0-1);
				ans += sum(incx0, x1-0, y1, x1-1, y0-1);
				ans += sum(incy1, x1, y0-0, x0-1, y0-1);
				ans += sum(incy0, x1, y1-0, x0-1, y1-1);
				io.out.println(ans);
			}
		}
	}
	
	int sum(int[][] v, int x1, int y1, int x0, int y0) {
		if (y0 < 0 || y1 >= v.length || x0 < 0 || x1 >= v[0].length) return 0;
		return v[y1][x1]-v[y1][x0]-v[y0][x1]+v[y0][x0];
	}
	
	/// TEMPLATE
	static int gcd(int n, int r) { return r == 0 ? n : gcd(r, n%r); }
	static long gcd(long n, long r) { return r == 0 ? n : gcd(r, n%r); }
	
	static <T> void swap(T[] x, int i, int j) { T t = x[i]; x[i] = x[j]; x[j] = t; }
	static void swap(int[] x, int i, int j) { int t = x[i]; x[i] = x[j]; x[j] = t; }

	void printArrayLn(int[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
	void printArrayLn(long[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
	
	static void dump(Object... o) { System.err.println(Arrays.deepToString(o)); } 
	
	void main() throws IOException {
		//		IOFast.setFileIO("rle-size.in", "rle-size.out");
		try { run(); }
		catch (EndOfFileRuntimeException e) { }
		io.out.flush();
	}
	public static void main(String[] args) throws IOException { new Main().main(); }
	
	static class EndOfFileRuntimeException extends RuntimeException {
		private static final long serialVersionUID = -8565341110209207657L; }

	static
	public class IOFast {
		private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		private PrintWriter out = new PrintWriter(System.out);

		void setFileIn(String ins) throws IOException { in.close(); in = new BufferedReader(new FileReader(ins)); }
		void setFileOut(String outs) throws IOException { out.flush(); out.close(); out = new PrintWriter(new FileWriter(outs)); }
		void setFileIO(String ins, String outs) throws IOException { setFileIn(ins); setFileOut(outs); }

		private static int pos, readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static char[] str = new char[500*8*2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static { for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; } isDigit['-'] = true; isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true; isLineSep['\r'] = isLineSep['\n'] = true; }
		public int read() throws IOException { if(pos >= readLen) { pos = 0; readLen = in.read(buffer); if(readLen <= 0) { throw new EndOfFileRuntimeException(); } } return buffer[pos++]; }
		public int nextInt() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; int ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
		public long nextLong() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; long ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
		public char nextChar() throws IOException { while(true) { final int c = read(); if(!isSpace[c]) { return (char)c; } } }
		int reads(int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } if(str.length == len) { char[] rep = new char[str.length * 3 / 2]; System.arraycopy(str, 0, rep, 0, str.length); str = rep; } str[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
		int reads(char[] cs, int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } cs[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
		public char[] nextLine() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isLineSep); try { if(str[len-1] == '\r') { len--; read(); } } catch(EndOfFileRuntimeException e) { ; } return Arrays.copyOf(str, len); }
		public String nextString() throws IOException { return new String(next()); }
		public char[] next() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); return Arrays.copyOf(str, len); }
//		public int next(char[] cs) throws IOException { int len = 0; cs[len++] = nextChar(); len = reads(cs, len, isSpace); return len; }
		public double nextDouble() throws IOException { return Double.parseDouble(nextString()); }
		public long[] nextLongArray(final int n) throws IOException { final long[] res = new long[n]; for(int i = 0; i < n; i++) { res[i] = nextLong(); } return res; }
		public int[] nextIntArray(final int n) throws IOException { final int[] res = new int[n]; for(int i = 0; i < n; i++) { res[i] = nextInt(); } return res; }
		public int[][] nextIntArray2D(final int n, final int k) throws IOException { final int[][] res = new int[n][]; for(int i = 0; i < n; i++) { res[i] = nextIntArray(k); } return res; }
		public int[][] nextIntArray2DWithIndex(final int n, final int k) throws IOException { final int[][] res = new int[n][k+1]; for(int i = 0; i < n; i++) { for(int j = 0; j < k; j++) { res[i][j] = nextInt(); } res[i][k] = i; } return res; }
		public double[] nextDoubleArray(final int n) throws IOException { final double[] res = new double[n]; for(int i = 0; i < n; i++) { res[i] = nextDouble(); } return res; }
	}
}