Finding Domino Tilings

Each domino has size 1×2 and consists of two 1×1 cells. Each cell contains one number from 0 to 6. There are 28 possible dominoes in total, one for each unordered pair (0,0), (0,1), ..., (6,6); the pairs (a,b) and (b,a) are the same domino.

You are given an 8×7 grid whose cells also contain numbers from 0 to 6. Cover the whole grid using all 28 dominoes exactly once. The two numbers covered by a placed domino must match the two numbers on that domino.

Dominoes may be rotated. The same domino cannot be used more than once. Count how many different placements can make the given grid.

The input consists of 8 lines. Each line is a string of length 7, and every character is a digit from 0 to 6.

Print the number of different domino placements that can make the given grid.