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(raw_input())
arr=map(int,raw_input().split())
small=1000000
index=0
fall=0

count=0
ans=0
for i in range(1,n):
    if(arr[i]<arr[i-1]):
        count+=1
        fall=i
if(arr[0]<arr[n-1] and count>0):
    fall=0
    count+=1
if(count==0):
    print 0
elif(count==1):
    print n-fall
else:
    print -1
