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())
l=list(map(int,input().split()))
l2=[]

m=l[0]
k=l[0]
for i in range(1,n):
    if l[i]>=k:
        k=l[i]
    else:
        l2=l[i:]
        break
# print(l2)
c=0
ans=0

if len(l2)>0:
    k2=l2[0] 
    if m>=k2:
        ans=1
    else:
        ans=-1



for i in range(1,len(l2)):
    if k2>l2[i] or l2[i]>m:
        ans=-1
        break
    else:
        ans+=1
        k2=l2[i]
if ans==-1:
    print("-1")
else:
    print(ans)