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
check = True
n = int(input())
nums = [int(x) for x in input().split()]
current = 0
res = 0
for i in range (n):
    if nums[i] < current:
        if check:
            check = False
            res = 1
        else:
            print(-1)
            exit()
    else:
        if not check:
            res += 1
    current = nums[i]
if check:
    print(0)
else:
    if nums[n - 1] <= nums[0]:
        print(res)
    else:
        print(-1)
