Flip a biased coin n times, heads with probability p. Return the expected number of adjacent positions where both flips were heads.

There are $n-1$ adjacent pairs and each is HH with probability $p^2$, so the answer is $(n-1)p^2$. The pairs overlap and are therefore dependent, which does not matter: expectation adds regardless.

Input

n = 10
p = 0.5

Output

2.25