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())
pos = list(map(int, input().split()))
x = pos[0]
i = 1
while i != n and pos[i] >= pos[i-1]:
    i += 1
k = 0
ans = n - i
for j in range(i+1, n):
    if pos[j] < pos[j-1]:
        k = 1
        break
if pos[n -1] > pos[0] and ans != 0:
    k = 1
if k == 1:
    print(-1)
else:
    print(ans)