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())
s=list(map(int,input().split()))
k=sorted(s)
m=min(s)
if m==s[0]:
    c=0
    s.reverse()
    for j in s:
        if j==m:
            c+=1
        else:
            break
    v=n-c
    s.reverse()
else:
    v=s.index(m)
x=s[v:n]
e=[]
for i in range(n-len(x)):
    e.append(s[i])
if s==k:
    print(0)
elif x+e==k:
    print(len(x))
else:
    print(-1)
