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 -*-
#ᕕ┌◕ᗜ◕┐ᕗ HELLO HELLO HELLO ᕕ┌◕ᗜ◕┐ᕗ

def allsame(a):
    x = a[0]
    for i in range(1,len(a)):
        if x != a[i]:
            return False
    return True

n = int(raw_input())
a = list(int(i) for i in raw_input().strip().split(" "))
d = 0
for i in range(n):
    if a[i] > a[(i+1)%n]:
        d += 1
if d >= 2:
    print -1
else:
    if allsame(a):
        print 0
    else:
        m = max(a)
        i = a.index(m)
        while a[(i+1)%n] == m:
            i += 1
        i %= n
        print n-i-1
