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
# It's cyclically sorted if we only experience one "jump" when going from
# the beginning to the end.  We mark the location of this jump.

n = int(raw_input())
A = [int(i) for i in raw_input().split()]

jump = None
can_do_it = True
for i in range(len(A) - 1):
    if A[i] > A[i + 1]:
        if jump is not None:
            can_do_it = False
            break
        else:
            jump = i + 1

if A[n - 1] > A[0]:
    if jump is not None:
        can_do_it = False
    else:
        jump = 0

if jump is None:
    print 0
elif can_do_it is False:
    print "-1"
else:
    print (n - jump) % n
