One day, Twilight Sparkle is interested in how to sort a sequence of integers a1, a2, ..., an 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, ..., an → an, a1, a2, ..., an - 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, ..., an (1 ≤ ai ≤ 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
# coding: utf-8
n = int(input())
a = [int(i) for i in input().split()]
for i in range(n):
    if i < n-1 and a[i+1]<a[i]:
        break
if i==n-1:
    ans = 0
else:
    ans = n-1-i
a = a[i+1:]+a[:i+1]
for i in range(n-1):
    if a[i] > a[i+1]:
        print(-1)
        break
else:
    print(ans)
