Problem: How many stars are there in the sky? A young programmer Polycarpus can't get this question out of his head! He took a photo of the starry sky using his digital camera and now he analyzes the resulting monochrome digital picture. The picture is represented by a rectangular matrix consisting of n lines each containing m characters. A character equals '1', if the corresponding photo pixel is white and '0', if it is black.

Polycarpus thinks that he has found a star on the photo if he finds a white pixel surrounded by four side-neighboring pixels that are also white: 
    
    
      
     1   
    111  
     1   
    

a star on the photo

Polycarpus whats to cut out a rectangular area from the photo and give his mom as a present. This area should contain no less than k stars. The stars can intersect, have shared white pixels on the photo. The boy will cut out the rectangular area so that its borders will be parallel to the sides of the photo and the cuts will go straight between the pixel borders.

Now Polycarpus keeps wondering how many ways there are to cut an area out of the photo so that it met the conditions given above. Help Polycarpus find this number.

Input

The first line of the input data contains three integers n, m and k (1 ≤ n, m ≤ 500;1 ≤ k ≤ nm). Then follow n lines, containing the description of the given photo as a sequence of lines. Each line contains m characters '0' or '1'.

Output

Print the required number of areas on the given photo.

Examples

Input

4 6 2
111000
111100
011011
000111


Output

6


Input

5 5 4
11111
11111
11111
11111
11111


Output

9

Note

We'll number the rows and columns below starting from 1, the coordinates (p, q) will denote a cell in row p, column q.

In the first sample Polycarpus should cut out any area containing a rectangle whose opposite corners lie in cells (1, 1) and (3, 4). Only rectangles with opposite corners in (1, 1) and (x, y), where x ≥ 3 and y ≥ 4 fit the conditions.

In the second sample any rectangle whose each side is no less than four, will do. The possible rectangle sizes are 4 × 4, 4 × 5, 5 × 4 and 5 × 5. Such figures can be cut in 4 ways, 2 ways, 2 ways and 1 way correspondingly.

Please do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use cin, cout streams or the %I64d specificator.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;

public class F implements Runnable {

	void solve() {
		int n = nextInt();
		int m = nextInt();
		int k = nextInt();
		if (n < 3 || m < 3) {
			out.println(0);
			return;
		}
		char[][] c = new char[n][];
		for (int i = 0; i < n; i++) {
			c[i] = nextToken().toCharArray();
		}
		int[][] isGood = new int[n - 2][m - 2];
		for (int i = 0; i < n - 2; i++) {
			for (int j = 0; j < m - 2; j++) {
				if (c[i][j + 1] == '1' && c[i + 1][j] == '1'
						&& c[i + 1][j + 1] == '1' && c[i + 1][j + 2] == '1'
						&& c[i + 2][j + 1] == '1') {
					isGood[i][j] = 1;
				}
			}
		}
		n -= 2;
		m -= 2;
		int[][] b = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				if (i > 0) {
					b[i][j] += b[i - 1][j];
				}
				if (j > 0) {
					b[i][j] += b[i][j - 1];
				}
				if (i > 0 && j > 0) {
					b[i][j] -= b[i - 1][j - 1];
				}
				b[i][j] += isGood[i][j];
			}
		}
		long ans = 0;
		for (int i = 0; i < n; i++) {
			for (int j = i; j < n; j++) {
				int cur = 0;
				for (int t = 0; t < m; t++) {
					while (cur < m && sum(b, i, t, j, cur) < k) {
						cur++;
					}
					ans += m - cur;
				}
			}
		}
		out.println(ans);
	}

	static int sum(int[][] a, int x1, int y1, int x2, int y2) {
		int ret = a[x2][y2];
		if (x1 > 0) {
			ret -= a[x1 - 1][y2];
		}
		if (y1 > 0) {
			ret -= a[x2][y1 - 1];
		}
		if (x1 > 0 && y1 > 0) {
			ret += a[x1 - 1][y1 - 1];
		}
		return ret;
	}

	FastScanner sc;
	PrintWriter out;

	public void run() {
		Locale.setDefault(Locale.US);
		try {
			sc = new FastScanner(System.in);
			out = new PrintWriter(System.out);
			solve();
			sc.close();
			out.close();
		} catch (Throwable e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	int nextInt() {
		return sc.nextInt();
	}

	String nextToken() {
		return sc.nextToken();
	}

	long nextLong() {
		return sc.nextLong();
	}

	double nextDouble() {
		return sc.nextDouble();
	}

	BigInteger nextBigInteger() {
		return sc.nextBigInteger();
	}

	class FastScanner extends BufferedReader {
		StringTokenizer st;
		boolean eof;
		String buf;
		String curLine;
		boolean createST;

		public FastScanner(String fileName) throws FileNotFoundException {
			this(fileName, true);
		}

		public FastScanner(String fileName, boolean createST)
				throws FileNotFoundException {
			super(new FileReader(fileName));
			this.createST = createST;
			nextToken();
		}

		public FastScanner(InputStream stream) {
			this(stream, true);
		}

		public FastScanner(InputStream stream, boolean createST) {
			super(new InputStreamReader(stream));
			this.createST = createST;
			nextToken();
		}

		String nextLine() {
			String ret = curLine;
			if (createST) {
				st = null;
			}
			nextToken();
			return ret;
		}

		String nextToken() {
			if (!createST) {
				try {
					curLine = readLine();
				} catch (Exception e) {
					eof = true;
				}
				return null;
			}
			while (st == null || !st.hasMoreTokens()) {
				try {
					curLine = readLine();
					st = new StringTokenizer(curLine);
				} catch (Exception e) {
					eof = true;
					break;
				}
			}
			String ret = buf;
			buf = eof ? "-1" : st.nextToken();
			return ret;
		}

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

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

		double nextDouble() {
			return Double.parseDouble(nextToken());
		}

		BigInteger nextBigInteger() {
			return new BigInteger(nextToken());
		}

		public void close() {
			try {
				buf = null;
				st = null;
				curLine = null;
				super.close();
			} catch (Exception e) {

			}
		}

		boolean isEOF() {
			return eof;
		}
	}

	public static void main(String[] args) {
		new F().run();
	}
}