Maximizing Values per Level in a Binary Tree

Given a binary tree, compute the maximum value at each level when traversed in level-order (i.e., breadth-first search). Formally, if the levels are denoted by \(L_0, L_1, L_2, \ldots\), for each level \(L_i\) find the maximum node value.

The tree is provided as a space‐separated list in level order, where the string null represents a missing node. For example, the input 1 3 2 5 3 null 9 corresponds to a tree in which the first level is just 1, the second level contains 3 and 2, and the third level contains 5, 3 (from the left subtree) and 9 (from the right subtree). Your task is to output the maximum value of each level, separated by spaces.

inputFormat

A single line of input containing the level-order traversal of the binary tree. Each node is separated by a space and missing nodes are represented by the string null.

Example: 1 3 2 5 3 null 9

outputFormat

A single line of output containing the maximum value at each level of the binary tree, separated by spaces. If the tree is empty, output an empty line.## sample

1 3 2 5 3 null 9

1 3 9