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 s(a, i):
   s = i
   while i+1 < len(a):
      if a[i] <= a[i+1]:
         i += 1
      else:
        return a[s:i+1]
   return a[s:i+1]

n = int(input())
a = list(map(int,input().split()))
b = s(a,0)
c = s(a,len(b))
if len(b) == n:
   print(0)
elif len(b) + len(c) == n and c[len(c)-1] <= b[0]:
    print(len(c))
else:
   print(-1)
