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(input())
mp = map(int,input().split())
a = []
for i in mp:
    a.append(i)

invp = 0
inve = 0
res = True
for i in range(1,n):
    if a[i]<a[i-1]:
        if invp==0:
            invp = i
        else:
            res = False
            break


if a[0]<a[n-1] and invp!=0:
    res = False

ans = (n-invp)%n
if res:
    print(ans)
else:
    print(-1)