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())

array = input()
array = list(map(int,array.split(" ")))

discordancias = 0
pos = 0

for i in range(1,n):
  if(array[i]<array[i-1]):
    discordancias+=1
    pos = i
  if(discordancias>1):
    break



if((array[n-1]>array[0] and discordancias>0) or discordancias>1):
  print(-1)
elif(discordancias==1):
  print(n-pos)
else:
  print(0)
