
49  ZOJ Monthly, December 2005  1002
A plane partition is a twodimensional array of integers n_{i,j} that are nonincreasing both from left to right and top to bottom. In other words,
n_{i,j} <= n_{i,j+1} Implicit in this definition is the requirement that the array be flush on top and to the left and contain no holes.
For example, one plane partition of 22 is illustrated above and the corresponding twodimensional array is
5 4 2 1 1 Now given 3 integers a, b, c, how many plane partitions whose diagrams fit inside an a * b rectangle and whose heights do not exceed c(in other words, with all n_{i,j} <= c)?
Input Each line contains 3 integers  a, b, c(0 < a, b, c <= 6). The input ends with EOF. Output Output the total number in one line for each test case. Sample Input 1 1 1 2 2 2 3 3 3 Sample Output 2 20 980 Author: ZHANG, Zheng 