Matrix of given integers


a1,1 a1,2 ... a1, n
a2,1 a2,2 ... a2, n
::
an, 1 an, 2 ... an, n


Then, create a program that outputs the maximum value of the sum of one or more consecutive terms (submatrix) in the vertical and horizontal directions and ends.



Input

The input data is given in the following format.


n
a1,1 a1,2 ... a1, n
a2,1 a2,2 ... a2, n
::
an, 1 an, 2 ... an, n


n is 1 or more and 100 or less, and ai, j is -10000 or more and 10000 or less.

Output

Print the maximum value on one line.

Examples

Input

3
1 -2 3
-4 5 6
7 8 -9


Output

16


Input

4
1 3 -9 2
2 7 -1 5
-8 3 2 -1
5 0 -3 1


Output

15
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	MyScanner sc = new MyScanner();
	Scanner sc2 = new Scanner(System.in);
	long start = System.currentTimeMillis();
	long fin = System.currentTimeMillis();
	final int MOD = 1000000007;
	int[] dx = { 1, 0, 0, -1 };
	int[] dy = { 0, 1, -1, 0 };

	int INF = Integer.MAX_VALUE / 2;

	void run() {
		int n = sc.nextInt();
		int[][] f = sc.nextInt2dArray(n, n);
		int[][] sum = new int[n][n];
		for (int i = 0; i < n; i++) sum[0][i] = f[0][i];
		for (int i = 0; i < n; i++) for (int j = 1; j < n; j++) sum[j][i] = sum[j - 1][i] + f[j][i];
		int ans = -INF;
		for (int i = 0; i < n; i++) {
			for (int j = i; j < n; j++) {
				int one = (i == 0) ? sum[j][0] : sum[j][0] - sum[i - 1][0];
				int[] dp = new int[n];
				Arrays.fill(dp, -INF);
				dp[0] = one;
				ans = Math.max(ans, dp[0]);
				for (int k = 1; k < n; k++) {
					int s = (i == 0) ? sum[j][k] : sum[j][k] - sum[i - 1][k];
					dp[k] = Math.max(dp[k - 1] + s, s);
					ans = Math.max(ans, dp[k]);
				}
			}
		}
		System.out.println(ans);
	}

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

	void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	void debug2(int[][] array) {
		for (int i = 0; i < array.length; i++) {
			for (int j = 0; j < array[i].length; j++) {
				System.out.print(array[i][j]);
			}
			System.out.println();
		}
	}

	boolean inner(int h, int w, int limH, int limW) {
		return 0 <= h && h < limH && 0 <= w && w < limW;
	}

	void swap(int[] x, int a, int b) {
		int tmp = x[a];
		x[a] = x[b];
		x[b] = tmp;
	}

	// find minimum i (a[i] >= border)
	int lower_bound(int a[], int border) {
		int l = -1;
		int r = a.length;
		while (r - l > 1) {
			int mid = (l + r) / 2;
			if (border <= a[mid]) {
				r = mid;
			} else {
				l = mid;
			}
		}
		// r = l + 1
		return r;
	}

	boolean palindrome(String s) {
		for (int i = 0; i < s.length() / 2; i++) {
			if (s.charAt(i) != s.charAt(s.length() - 1 - i)) {
				return false;
			}
		}
		return true;
	}

	class MyScanner {
		int nextInt() {
			try {
				int c = System.in.read();
				while (c != '-' && (c < '0' || '9' < c))
					c = System.in.read();
				if (c == '-')
					return -nextInt();
				int res = 0;
				do {
					res *= 10;
					res += c - '0';
					c = System.in.read();
				} while ('0' <= c && c <= '9');
				return res;
			} catch (Exception e) {
				return -1;
			}
		}

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

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

		String next() {
			try {
				StringBuilder res = new StringBuilder("");
				int c = System.in.read();
				while (Character.isWhitespace(c))
					c = System.in.read();
				do {
					res.append((char) c);
				} while (!Character.isWhitespace(c = System.in.read()));
				return res.toString();
			} catch (Exception e) {
				return null;
			}
		}

		int[] nextIntArray(int n) {
			int[] in = new int[n];
			for (int i = 0; i < n; i++) {
				in[i] = nextInt();
			}
			return in;
		}

		int[][] nextInt2dArray(int n, int m) {
			int[][] in = new int[n][m];
			for (int i = 0; i < n; i++) {
				in[i] = nextIntArray(m);
			}
			return in;
		}

		double[] nextDoubleArray(int n) {
			double[] in = new double[n];
			for (int i = 0; i < n; i++) {
				in[i] = nextDouble();
			}
			return in;
		}

		long[] nextLongArray(int n) {
			long[] in = new long[n];
			for (int i = 0; i < n; i++) {
				in[i] = nextLong();
			}
			return in;
		}

		char[][] nextCharField(int n, int m) {
			char[][] in = new char[n][m];
			for (int i = 0; i < n; i++) {
				String s = sc.next();
				for (int j = 0; j < m; j++) {
					in[i][j] = s.charAt(j);
				}
			}
			return in;
		}
	}
}