CF215C Crosses

There is a board with a grid consisting of $ n $ rows and $ m $ columns, the rows are numbered from $ 1 $ from top to bottom and the columns are numbered from $ 1 $ from left to right. In this grid we will denote the cell that lies on row number $ i $ and column number $ j $ as $ (i,j) $ . A group of six numbers $ (a,b,c,d,x_{0},y_{0}) $ , where $ 0

The input consists of a single line containing three integers $ n $ , $ m $ and $ s $ ( $ 1

Print a single integer — the number of distinct groups of six integers that denote crosses with area $ s $ and that are fully placed on the $ n×m $ grid. Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

In the first sample the sought groups of six numbers are: $ (0,0,0,0,1,1) $ , $ (0,0,0,0,1,2) $ , $ (0,0,0,0,2,1) $ , $ (0,0,0,0,2,2) $ . In the second sample the sought groups of six numbers are: $ (0,1,1,0,2,2) $ , $ (0,1,1,0,2,3) $ , $ (1,0,0,1,2,2) $ , $ (1,0,0,1,2,3) $ .