Splendid Spangles

(1995 ACS Problem D)

Spangles are terrific little sweets that come in five flavours; apple, blueberry, cherry, date and eucalyptus. The are so popular because millions of new flavours can be created by eating different combinations of Spangles.

Being a curious person, you are interested in finding out how many distinct combinations of flavours can be formed from a specific number of Spangles. Of course, eating an apple and a cherry Spangle at the same time is equivalent to eating two apple and two cherry Spangles, so these are not distinct combinations.

You must write a program which determines f(n), the number of distinct flavours that can be made by eating up to and including n Spangles, for each value of n from 1 to 50 inclusive.

INPUT

There is no input.

OUTPUT

There are exactly 50 lines of output. The nth line of output has two numbers, n and f(n), separated by a single space. The sample output below shows the first four lines of output.

SAMPLE OUTPUT

This shows only the first four lines of output.

1 5
2 15
3 45
4 100