Mike is the president of country What-The-Fatherland. There are *n* bears living in this country besides Mike. All of them are standing in a line and they are numbered from 1 to *n* from left to right. *i*-th bear is exactly *a*<sub class="lower-index">*i*</sub> feet high. 

A group of bears is a non-empty contiguous segment of the line. The size of a group is the number of bears in that group. The strength of a group is the minimum height of the bear in that group.

Mike is a curious to know for each *x* such that 1 ≤ *x* ≤ *n* the maximum strength among all groups of size *x*.
The first line of input contains integer *n* (1 ≤ *n* ≤ 2 × 10<sup class="upper-index">5</sup>), the number of bears.

The second line contains *n* integers separated by space, *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*n*</sub> (1 ≤ *a*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">9</sup>), heights of bears.
def task2(childs: list) -> list:
    """
    Parameters:
    :pandas (list): panda heights list
    :return: list of maximum group powers
    """
    n = len(childs)
    
    answer = [max(childs)]
    buffer = childs.copy()

    for i in range(2, n + 1):
        max_ = buffer[0] = min(buffer[0], childs[i - 1])
        
        for j in range(1, n - i + 1):
            buffer[j] = min(buffer[j], childs[i + j - 1])
            max_ = max(max_, buffer[j])

        answer.append(max_)

    return answer
