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
#!/usr/bin/env python
# coding: utf-8

# In[ ]:


n=int(input())
num = [int(x) for x in input().split()] 
for i in range(0,n):

    if(num[i]<num[i-1]):
        p=num[i:]
        q=num[:i]
        break

d=sorted(num)

if(num==d):
    print("0")
elif(d==p+q): 
    print(len(p))
else:
    print("-1")


# In[ ]:




