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
nums = map(int, raw_input('').split(' '))
nums = map(int, raw_input('').split(' '))
n = len(nums)
stop_pos = 0
while stop_pos < (n - 1):
    if nums[stop_pos] > nums[stop_pos + 1]:
        break
    stop_pos += 1


def is_increasing(nums, start):
    for i in xrange(start, len(nums) - 1):
        if nums[i] > nums[i + 1]:
            return False
    return True

if stop_pos == n - 1:
    print 0
elif is_increasing(nums, stop_pos + 1) and nums[n - 1] <= nums[0]:
    print n - stop_pos - 1
else:
    print -1
