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')
elif a == sorted(a,reverse = True):
    if n == 2:
        print(n-1)
    else:
        print('-1')
else:
    limit = a[0]
    if a[1] < a[0]:
        if a[1:] == sorted(a[1:]) and a[len(a) - 1] <= limit:
            print (len(a[1:]))
        else:
            print('-1')
    else:
        ct = 0
        pos = -1
        for x in range(1,len(a)-1):
            if a[x] >= a[x-1] and a[x] > a[x+1]:
                ct += 1
                pos = x
        if ct == 1 and a[pos+1:] == sorted(a[pos+1:]) and a[len(a) - 1] <= limit:
            print (len(a[pos+1:]))
        else:
            print ('-1')