One day, Twilight Sparkle is interested in how to sort a sequence of integers $*a*_{1}, *a*_{2}, ..., *a*_{*n*}$ in non-decreasing order. Being a young unicorn, the only operation she can perform is a unit shift. That is, she can move the last element of the sequence to its beginning:

$*a*_{1}, *a*_{2}, ..., *a*_{*n*} → *a*_{*n*}, *a*_{1}, *a*_{2}, ..., *a*_{*n* - 1}.$

Help Twilight Sparkle to calculate: what is the minimum number of operations that she needs to sort the sequence?

Input

The first line contains an integer $*n*$ $(2 ≤ *n* ≤ 10^{5})$. The second line contains $*n*$ integer numbers $*a*_{1}, *a*_{2}, ..., *a*_{*n*}$ $(1 ≤ *a*_{*i*} ≤ 10^{5})$.

Output

If it's impossible to sort the sequence output -1. Otherwise output the minimum number of operations Twilight Sparkle needs to sort it.