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
#!/usr/bin/python

from sys import stdin

def Check(a):
    i = 1
    while i < n:
        if a[i-1] > a[i]:
            return False
        i += 1
    return True

n = int(stdin.readline())
a = map(int, stdin.readline().split())

c = 0
l = 0
i = 0
while i < n:
    j = i+1
    while j < n and a[j-1] <= a[j]:
        j += 1
    c += 1
    l = j-i
    i = j

a = a[(n-l):]+a[:(n-l)]

if c == 1:
    l = 0

if c > 2 or not Check(a):
    l = -1

print l
