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
a=int(input())
s=[int(i) for i in input().split()]
i=0
c=0
if sorted(s)==s:
    print(0)
else:
    if s[-1]>s[0]:
        print(-1)
    else:
        while(s[i+1]>=s[i]):
            i+=1
        for j in range(i+1,len(s)-1):
            if s[j+1]<s[j]:
                break
            else:
                c+=1
        if c==(len(s)-i-2):
            print(len(s)-i-1)
        
        else:
            print(-1)