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 = input()
n = int(n)

d = [int(x) for x in input().split(' ')]

e = 0
f = 0
for i in range(1, n):
    if d[i-1] <= d[i]:
        if f == 0:
            pass
        else:
            if d[i] <= d[0]:
                pass
            else:
                e = -1
                break
    else:
        if (f == 0) and (d[0] >= d[i]):
            f = 1
            e = i
        else:
            e = -1
            break
    #print(e)
if e == -1:
    print(-1)
else:
    print((n-e)%n)