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())
a=list(map(int,input().split()))
#for x in range(len(a)):
#    a[x]=int(a[x])
# print(x)
ans=0
d=0
for x in range(1,n):
    if(a[x-1]>a[x]):
        d=1
        if(sorted(a)==a[x:]+a[:x]):
            ans=n-x
        else:
            ans=-1
        break
if(d==0):
    print(0)
else:
    print(ans)