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())
arr=list(map(int,input().split()))
minn=min(arr)
maxx=max(arr)
k=-1
for i in range(0,len(arr)-1):
    if(arr[i]==maxx and arr[i+1]==minn):
        k=i 
        break 
if(arr[len(arr)-1]==maxx and arr[0]==minn):
    k=0
if(k==-1):
    print(-1)
else:
    bef=arr[:k+1]
    af=arr[k+1:]
    if(sorted(arr)==arr):
        print(0)
    elif(sorted(bef)==bef and sorted(af)==af and arr[0]>=arr[len(arr)-1]):
        print(len(arr)-k-1)
    else:
        print(-1)
