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.
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 B and 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 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 the minimum cost.
2 2 2 WW WW BB BB 1 1 1 1 2 2 2 2
5
