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
def f(n):
    s = map(int, raw_input().split())
    _s = sorted(s)
    if list(s) == list(_s):
        print 0
    else:
        idx = -1
        count = 0
        for i in xrange(n-1):
            if s[i] > s[i+1]:
                count += 1
                idx = i
                if count > 1:
                    print -1
                    return
        if sorted(s[idx+1:]+s[0:idx+1]) == list(s[idx+1:]+s[0:idx+1]):
            print n-idx-1
        else:
            print -1
n = int(raw_input())
f(n)