An undirected graph is given. Each edge of the graph disappears with a constant probability. Calculate the probability with which the remained graph is connected.

The first line contains three integers `N` (`1 \leq N \leq 14`), `M` (`0 \leq M \leq 100`) and `P` (`0 \leq P \leq 100`), separated by a single space.
`N` is the number of the vertices and `M` is the number of the edges. `P` is the probability represented by a percentage.

The following `M` lines describe the edges.
Each line contains two integers `v_i` and `u_i` (`1 \leq u_i, v_i \leq N`).
(`u_i, v_i`) indicates the edge that connects the two vertices `u_i` and `v_i`.

Output a line containing the probability with which the remained graph is connected.
Your program may output an arbitrary number of digits after the decimal point. However, the absolute error should be `10^{-9}` or less.

3 3 50 1 2 2 3 3 1

0.500000000000

3 3 10 1 2 2 3 3 1

0.972000000000

4 5 50 1 2 2 3 3 4 4 1 1 3

0.437500000000

Source: ACM-ICPC Japan Alumni Group Winter Contest 2012
, Tokyo, Japan, 2012-03-10

http://acm-icpc.aitea.net/

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