B. Little Pony and Sort by Shift
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 ≤ 105). The second line contains n integer numbers a 1, a 2, ..., 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.

Examples
Input
2
2 1
Output
1
Input
3
1 3 2
Output
-1
Input
2
1 2
Output
0