Graph
Let's consider undirected graph with N vertices and M edges. How many different ways are there to paint it, if there are only K colours? You need not use all colours in one painting. Two paintings are considered the same if there is such a renumbering of vertices of one painting that leaves the list of edges unchanged, and the colour of its i^th vertex is the same as the colour of i^th vertex of other painting for each i. For example, paintings on picture are the same (renumbering: 1 → 1, 2 → 2, 3 →4, 4 → 3).
Input
First line of input file contains three integer numbers: N, M and K (1 ≤ N ≤ 9, 1 ≤ M ≤ 100, 1 ≤ K ≤ 10). Next M lines contain two integers each - graph edges. Graph may contain parallel edges and loops. Numbers in lines are separated by spaces.
Output
Output file must contain one integer number R - answer for the task.
