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(int, raw_input().split())

left = 0
while left < n-1 and a[left] <= a[left+1]:
    left += 1

lh = left+1
while lh < n-1 and a[lh] <= a[lh+1]:
    lh += 1

if left == n-1:
    print 0

elif lh == n-1:
    if a[n-1] <= a[0]:
        print n-left-1
    else:
        print -1
else:
    print -1