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
#define _USE_MATH_DEFINES
#define _CRT_SECURE_NO_DEPRECATE

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <climits>
#include <cfloat>
#include <ctime>
#include <cassert>
#include <map>
#include <utility>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <vector>
#include <algorithm>
#include <functional>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <numeric>
#include <list>
#include <iomanip>
#include <fstream>


using namespace std;
const int MOD = 1000000009; // check!!!
const int INF = 100000000; //1e8

typedef long long ll;
typedef pair<int,int> Pii;
typedef pair<ll,ll> Pll;

#define FOR(i,n) for(int i = 0; i < (n); i++)
#define sz(c) ((int)(c).size())
#define ten(x) ((int)1e##x)
#define tenll(x) ((ll)1e##x)

int a[100][100];
int b[101][101];

int main(){

	int n; cin>>n;
	FOR(i,n) FOR(j,n) cin>>a[i][j];

	int ans = -INF;
	FOR(i,n){
		int s[101] = {};
		FOR(j,n) s[j+1] = s[j] + a[i][j];
		FOR(j,n) for(int k = j; k < n; k++){
			b[j][k] = max(0,b[j][k]) + s[k+1] - s[j];
			ans = max(ans,b[j][k]);
		}
	}

	cout << ans << endl;

	return 0;
}