The six sides of $a$ convex hexagon A1A2A3A4A5A6 are colored red. Each of the diagonals of the hexagon is colored either red or blue. If N is the number of colorings such that every triangle AiAjAk, where 1 $\le$ I < j < $k$ $\le$ 6, has at least one red side, find the sum of the squares of the digits of N.

Step 1: Number of ways such that atleast one side of

Step 2: A2A4A6 is red = 3C1 × 22 – 3C2 × 2 + 3C3 20

Step 3: Number of ways such that atleast one side of

Step 4: A1A3A5 is red = 7

Step 5: Number of ways to colour diagonals A1A4, A2A5,

Step 6: A3A6 = 23 = 8

Step 7: => Required number = 8 × 7 × 7

Step 8: => Sum of square of digits = 32 + 92 + 22