One day, Twilight Sparkle is interested in how to sort a sequence of integers a₁, a₂, ..., 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:

a₁, a₂, ..., a_n → a_n, a₁, a₂, ..., 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 ≤ 10⁵). The second line contains n integer numbers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁵).

Output

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

Little Pony and Sort by Shift

Examples