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
n = int(input())
a = list(map(int, input().split()))

if a == sorted(a):
    print(0)
else:
    m = a.index(max(a))
    
    while m < n-1:
        if a[m] == a[m+1]:
            m += 1
        else:
            break
    
    a1 = a[:m+1]
    a2 = a[m+1:]
    
    if a1 == sorted(a1) and a2 == sorted(a2) and max(a2) <= a1[0]:
        print(n-(m+1))
    else:
        print(-1)