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
input()
lst = [int(x) for x in input().split()]
def canSort(lst):
    l = 0
    start = -1
    for i in range(len(lst)):
        if l == 0:
            if i > 0:
                if lst[i-1] > lst[i]:
                    l = 1
                    start = i
                    if lst[start]>lst[0]:
                        return -1
        elif l == 1:
            if lst[i-1] > lst[i] or lst[i] > lst [0]: 
                return -1
    return len(lst)-start if start != -1 else 0
print (canSort(lst))
