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
# cook your dish here
n=int(input())
l=[int(y) for y in input().split()]
if(n==1):
    print(0)
elif n==2:
    if l[0]<=l[1]:
        print(0)
    else:
        print(1)
else:
    i=0
    while i<n-1:
        if l[i]<=l[i+1]:
            i+=1
        else:
            break
    if i==n-1:
        print(0)
    else:
        c=0
        check=0
        j=i+1
        while j<n-1:
            if l[j]<=l[j+1] and l[j]<=l[0]:
                c+=1
                j+=1
            else:
                check=1
                break
            
        if l[n-1]<=l[0]:
            c+=1
            if(check==1):
                print(-1)
            else:
                print(c)
        else:
            print(-1)
        
            
                