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Competitions

October 7 - BMTK Programming School, High League

Function Run Fun

We all love recursion! Don't we?

Consider a three-parameter recursive function w(a, b, c):

if a < = 0 or b < = 0 or c < = 0, then w(a, b, c) return 1

if a > 20 or b > 20 or c > 20, then w(a, b, c) return w(20, 20, 20)

if a < b and b < c, then w(a, b, c) return w(a, b, c - 1) + w(a, b- 1, c - 1) - w(a, b - 1, c)

otherwise return w(a - 1, b, c) + w(a - 1, b - 1, c) + w(a - 1, b, c - 1) - w(a - 1, b - 1, c - 1)

prb2177.gif

This is an easy function to implement. The problem is, if implemented directly, for moderate values of a, b and c (for example, a = 15, b = 15, c = 15), the program takes hours to run because of the massive recursion.

Input

Contains series of integer triples, one per line, until the flag of -1 -1 -1. Using the above technique, you are to calculate w(a, b, c) efficiently and print the result.

Output

Print the value for w(a, b, c) for each triple.

Time limit 1 second
Memory limit 128 MiB
Input example #1
1 1 1
2 2 2
10 4 6
50 50 50 
-1 7 18
-1 -1 -1
Output example #1
w(1, 1, 1) = 2
w(2, 2, 2) = 4
w(10, 4, 6) = 523
w(50, 50, 50) = 1048576
w(-1, 7, 18) = 1