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
# 3 4 5 2 1
#       ^
# 2 3 4 1 2
# 0 1 2 3 4

# 3 1 2
#
def main():
    n = int(raw_input())
    seq = map(int, raw_input().split())

    idx = 1
    breakpoint = -1
    while idx < n:
        if seq[idx] < seq[idx-1]:
            breakpoint = idx
            break
        idx+=1

    if idx == n:
        print 0
        return

    smallest = seq[0]
    for i in xrange(n-1, breakpoint-1, -1):
        if seq[i] > smallest:
            print -1
            return
        smallest = seq[i]

    print n-breakpoint

main()
