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 get_res(N, L):
    result = 0
    s = min(L)
    min_index = 0
    for i in range(N-1):
        if L[i] != s and L[i+1] == s:
            min_index = i+1

    #print "min index: ", min_index

    for j in range(min_index, min_index+N-1):
        #k = j % N
        if L[(j+1)%N]-L[j%N] < 0:
            return -1
    result = (N - min_index)%N
    return result

N = int(raw_input())  

L = [int(s) for s in raw_input().split(" ")]
result = get_res(N, L)
print "{}".format(result)
