Small John is playing a dice stacking game. Six faces of a die are squares of the same size; each face of a die has a number range from 1 to 6.
The dice game is to stack several dice up with arbitrary order. You must keep the following rule: For each pair of consecutive dice, the number on the bottom of the top die must match the number on the top of the bottom die. In other words, the two faces that are together must have the same number.
Then a long rectangular pillar, which has 4 sides, is created. We are trying to make one side have the maximum sum. (Note that after we rotate a die to fix the top face and bottom face, we can still rotate the die by 90, 180, or 270 degrees.) Write a program to find the maximum sum that one side can have.