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 linear_search(A):
    for i in range(0,len(A)-1):
        if A[i] > A[i+1]:
            return i+1
    return -1


def solve():
    n = input()
    A = map(int, raw_input().split())
    i = linear_search(A)
    if i != -1:
        B = A[i:]+A[0:i]
        if sorted(A) == B:
            print n - i
        else:
            print -1
    else:
        if sorted(A) == A:
            print 0
        else:
            print -1

solve()