Maximum Sum Sequence II

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

inputFormat

outputFormat

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

样例

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

16