Triplets

Given three ranges of integers ([a, A]), ([b, B]), and ([c, C]), determine the total number of ordered triples of integers ((x, y, z)) that satisfy the following conditions:

• (x $\ne$ y)

• (x $\ne$ z)

• (y $\ne$ z)

• (a $\le$ x $\le$ A)

• (b $\le$ y $\le$ B)

• (c $\le$ z $\le$ C)

Input

The first line of the input contains the integer (N). The second line contains (N) integers, separated by spaces, representing the sequence ((a, A, b, B, c, C)) where (a $\le$ A), (b $\le$ B), (c $\le$ C), and (-10^3 $\le$ a, b, c, A, B, C $\le$ 10^3).

Output

Output a single line containing the answer to the problem.

Examples