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
#imgur.com/Pkt7iIf.png

#n, m = map(int, input().split())
#n = int(input())
#d = list(map(int, input().split()))

def issorted(d):
    for i in range(1, len(d)):
        if d[i-1] > d[i]:
            return False
    return True

n = int(input())
d = list(map(int, input().split()))

if issorted(d): print(0)

for i in range(1, n):
    if d[i-1] > d[i]:
        p = d[i:] + d[:i]
        if issorted(p):
            print(n - i)
            break
        else:
            print(-1)
            break
