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())
a = list(map(int, input().split()))
a = a + a
cn = 1
for i in range(2 * n - 2, 0, -1):
  if a[i] <= a[i + 1]:
    cn += 1
  else:
    cn = 1
  if cn == n:
    print(n - i)
    exit()
print(-1)
exit()

n = int(input())
print("\n".join('*'*abs(i) + 'D'*(n - 2 * abs(i)) + '*'*abs(i) for i in range(-(n // 2), n // 2 + 1)))
exit()

s = input()
if len(s) > 2:
  s = s[-2:]
n = int(s)
print((1 + 2**n + 3**n + 4**n) % 5)
exit()


n = int(input())
for i in range(n):
  x, y = map(int, input().split())
  if x != y:
    print('Happy Alex')
    exit()
print('Poor Alex')
