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
def solve(n, a):
    j = 0
    for i in xrange(n):
        if i > 0 and a[i-1] > a[i]:
            j = i
            break
    else:
        print 0
        return

    a = a[j:] + a[:j]
    for i in xrange(n):
        if i > 0 and a[i-1] > a[i]:
            print -1
            return
    else:
        print n - j

if __name__ == '__main__':
    n = int(raw_input())
    a = [int(x) for x in raw_input().split()]

    solve(n, a)
