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()))
s=a.copy()
s.sort()
ind=0
if(s[0]==s[n-1]):
    print(0)
elif(a[n-1]>a[0]):
    if(a!=sorted(a)):
        print(-1)
    else:
        print(0)
else:
    f=0
    for i in range(0,n-1):
        t=a[i+1]-a[i]
        if(t<0):
            f+=1
        if(f==2):
            break   
    if(f==2): 
        print(-1)
    else:
        for i in range(n-1,0,-1):
            if(a[i]==s[0] and a[i-1]!=s[0]):
                ind=i
                break
        print(n-ind)