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(' ')))
i=0
if len(L)<1:
  print(0)
else:
  while i+1<len(L) and L[i]<=L[i+1]:
    i=i+1
  j=i+1
  k=0
  
  while j<len(L) and L[j]<=L[0] and L[j]<=L[(j+1)%n]:
    j=j+1
    k=k+1
  if j!=n:
    print(-1)
  else:
    print(k)
  