Reachable Cells

Problem F and F2 are the same problem, but with different constraints and time limits.

We have a board divided into N horizontal rows and N vertical columns of square cells. The cell at the i-th row from the top and the j-th column from the left is called Cell (i,j). Each cell is either empty or occupied by an obstacle. Also, each empty cell has a digit written on it. If A_{i,j}= 1, 2, ..., or 9, Cell (i,j) is empty and the digit A_{i,j} is written on it. If A_{i,j}= #, Cell (i,j) is occupied by an obstacle.

Cell Y is reachable from cell X when the following conditions are all met:

• Cells X and Y are different.
• Cells X and Y are both empty.
• One can reach from Cell X to Cell Y by repeatedly moving right or down to an adjacent empty cell.

Consider all pairs of cells (X,Y) such that cell Y is reachable from cell X. Find the sum of the products of the digits written on cell X and cell Y for all of those pairs.

Constraints

• 1 \leq N \leq 500
• A_{i,j} is one of the following characters: 1, 2, ... 9 and #.

Input

Input is given from Standard Input in the following format:

N A_{1,1}A_{1,2}...A_{1,N} A_{2,1}A_{2,2}...A_{2,N} : A_{N,1}A_{N,2}...A_{N,N}

Output

Print the sum of the products of the digits written on cell X and cell Y for all pairs (X,Y) such that cell Y is reachable from cell X.

Examples

Input

2 11 11

Output

5

Input

4 1111 11#1 1#11 1111

Output

47

Input

10 76##63##3# 8445669721 75#9542133 3#285##445 749632##89 2458##9515 5952578#77 1#3#44196# 4355#99#1# 298#63587

Output

36065

Input

10 4177143673 7######### 5#1716155# 6#4#####5# 2#3#597#6# 6#9#8#3#5# 5#2#899#9# 1#6#####6# 6#5359657# 5#########

Output

6525

inputFormat

Input

Input is given from Standard Input in the following format:

N A_{1,1}A_{1,2}...A_{1,N} A_{2,1}A_{2,2}...A_{2,N} : A_{N,1}A_{N,2}...A_{N,N}

outputFormat

Output

Print the sum of the products of the digits written on cell X and cell Y for all pairs (X,Y) such that cell Y is reachable from cell X.

Examples

Input

2 11 11

Output

5

Input

4 1111 11#1 1#11 1111

Output

47

Input

10 76##63##3# 8445669721 75#9542133 3#285##445 749632##89 2458##9515 5952578#77 1#3#44196# 4355#99#1# 298#63587

Output

36065

Input

10 4177143673 7######### 5#1716155# 6#4#####5# 2#3#597#6# 6#9#8#3#5# 5#2#899#9# 1#6#####6# 6#5359657# 5#########

Output

6525

样例

4
1111
11#1
1#11
1111

47