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=[int(x) for x in input().split()]
count=0
if a==sorted(a):
    print(0)
else:
    p=min(a)
    for i in range(n):
        if a[(i+1)%n]-a[i]<0:
            count+=1
        if count>1:
            print(-1)
            break
    if count<=1:
        if a[0]==a[n-1]==p:
            j=n-1
            fl=0
            while p==a[j]:
                j-=1
                fl+=1
            print(fl)
        else:
            print(n-a.index(p))
