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 = input().split(' ')

pos = -1
valid = True
for i in range(len(a)):
    if (i + 1 < len(a)):
        if (int(a[i]) > int(a[i + 1])):
            if (pos == -1):
                pos = i + 1
            else:
                valid = False
if (valid and pos == -1):
    pos = 0
ans = pos
if (valid):
    for i in range(len(a) - 1):
        n_pos = (int(pos) + 1) % n
        if (int(a[pos]) > int(a[n_pos])):
            valid = False
        pos = n_pos

if (valid):
    print((n - ans) % n)
else:
    print(-1)