Given a cubic lattice of size $N \times M\times L$ such that each lattice point $(i,j,k)$ is either white or black. The coordinates of the lattice point are all positive integers. Let the cost of flipping the color of lattice point $(i,j,k)$ be $a_{i,j,k}$. Find the minimum cost to flip the colors of lattice points such that the bottom left corner $(1,1,1)$ is black, the top right corner $(N,M,L)$ is white, and any two different lattice points $(i_1, j_1, k_1)$ and $(i_2,j_2,k_2)$ satisfy at least one of the following conditions.

Input

The first line includes three integers $N, M, L$ ($1\le N, M, L\le 5\times 10^3$, $2 \leq N \times M \times L \leq 5\times 10^3$), denoting the size of the lattice. Each of the next $L \times N$ lines contains a string of length $M$ that only consists of \t{B} and \t{W}. The initial color of lattice point $(i,j,k)$ is the $j$-th character of the $(k-1) \times N + i$ line. If the character is \t{B}, it means the color of the lattice point is black, otherwise it is white. Each of the next $L \times N$ lines contains $M$ non-negative integers not greater than $10^5$. The cost of flipping the color of lattice point $(i,j,k)$ is the $j$-th integer of the $(k-1) \times N + i$ line.

Output

Output the minimum cost.

Example

2 2 2
WW
WW
BB
BB
1 1
1 1
2 2
2 2

5