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()))
m = a[0]
mi = 0
dip = False
has_result = True
for i in range(1, n):
    if a[i] >= m and not dip:
        m = a[i]
        mi = i
    if a[i] < a[i-1]:
        if dip:
            has_result = False
            break
        else:
            dip = True

    if dip and a[i] > a[0]:
        has_result = False
        break
if has_result:
    print(n-1 - mi)
else:
    print(-1)