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(raw_input())
a = map(lambda x: int(x), raw_input().split())

nds = [0]
for i in range(1, len(a)):
    if a[i] < a[i - 1]:
        nds.append(i)

if len(nds) > 2:
    print -1
elif len(nds) == 1:
    print 0
else:
    st = nds[1]
    if min(a[0:st]) >= max(a[st:]):
        print n - st
    else:
        print -1


