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
def shift(arr):
    k=arr[-1]
    n=len(arr)
    for i in range(n-1):
        arr[n-1-i]=arr[n-1-i-1]
    arr[0]=k
def proB(arr):
    c=0
    s=0
    n=len(arr)
    for i in range(len(arr)-1):
        if(arr[i]>arr[i+1]):
            s=i+1
            c+=1
    if(c==0):
        print(0)
        return 
    if(arr[0]<arr[-1]):
        c+=1
    if(c>=2):
        print(-1)
    else:
        print(n-s)
n=int(input())
arr=list(map(int,input().split()))
proB(arr)