A. Relations @ DSAP Vietnam Contest @ Timus Online Judge

A. Relations

Time limit: 1.0 second
Memory limit: 64 MB

Consider a specific set of comparable objects. Between two objects a and b, there exits one of the following three classified relations:

a = b
a < b
b < a

Because relation '=' is symmetric, it is not repeated above.

So, with 3 objects (a, b, c), there can exist 13 classified relations:

a = b = c a = b < c c < a = b a < b = c
b = c < a a = c < b b < a = c a < b < c
a < c < b b < a < c b < c < a c < a < b
c < b < a

Given N, determine the number of different classified relations between N objects.

Includes many integers N (in the range from 2 to 10), each number on one line. Ends with −1.

For each N of input, print the number of classified relations found, each number on one line.

input	output
2 3 -1	3 13