Nicholas has an array a that contains n distinct integers from 1 to n. In other words, Nicholas has a permutation of size n.

Nicholas want the minimum element (integer 1) and the maximum element (integer n) to be as far as possible from each other. He wants to perform exactly one swap in order to maximize the distance between the minimum and the maximum elements. The distance between two elements is considered to be equal to the absolute difference between their positions.

Input

The first line of the input contains a single integer n (2 ≤ n ≤ 100) — the size of the permutation.

The second line of the input contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ n), where ai is equal to the element at the i-th position.

Output

Print a single integer — the maximum possible distance between the minimum and the maximum elements Nicholas can achieve by performing exactly one swap.

Examples

Input

5
4 5 1 3 2


Output

3


Input

7
1 6 5 3 4 7 2


Output

6


Input

6
6 5 4 3 2 1


Output

5

Note

In the first sample, one may obtain the optimal answer by swapping elements 1 and 2.

In the second sample, the minimum and the maximum elements will be located in the opposite ends of the array if we swap 7 and 2.

In the third sample, the distance between the minimum and the maximum elements is already maximum possible, so we just perform some unnecessary swap, for example, one can swap 5 and 2.
def main():
    number_of_elements = int(input())
    nicholas_lst = [int(i) for i in input().split()]

    max_idx = nicholas_lst.index(max(nicholas_lst))
    min_idx = nicholas_lst.index(min(nicholas_lst))
    len_lst = len(nicholas_lst)
    distance = abs(max_idx - min_idx)

    max_distance = 0

    if distance == (len_lst - 1):
        return len_lst - 1

    if max_idx > min_idx:
        distance_from_max_to_end = len_lst - max_idx
        distance_from_min_to_start = min_idx
        if distance_from_max_to_end > distance_from_min_to_start:
            # swap max_idx to end of lst
            return len_lst - min_idx - 1
        # swap min_idx to start of lst
        return max_idx

    # start - max_idx - min_idx - end
    distance_from_min_to_end = len_lst - min_idx
    distance_from_max_to_start = max_idx
    if distance_from_min_to_end > distance_from_max_to_start:
        # swap min_idx to end of lst
        return len_lst - max_idx - 1
    # swap min_idx to start of lst
    return min_idx

print(main())

