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())
x = list(map(int, input().split()))
flag, cnt, prev_max, prev_min = 0, 0, 0, x[0]
if n == 2:
    if x[0] <= x[1]:
        print(0)
    else:
        print(1)
else:
    for i in range(1, n):
        if flag == 0:
            if x[i] < x[i - 1]:
                flag = 1
                cnt += 1
                prev_max = x[i - 1]
                if x[i] > prev_min:
                    cnt = -1
                    break
        elif flag == 1:
            if prev_max >= x[i] >= x[i - 1]:
                cnt += 1
            if x[i] < x[i - 1] or x[i] > prev_max or x[i] > prev_min:
                cnt = -1
                break
    print(cnt)
