Symmetric Sum in a Binary Tree

You are given a binary tree represented in level order. Some nodes may be missing; these are denoted by -1 in the input. Your task is to compute the symmetric sum for each level of the tree.

For each level, if the level has n nodes with values a₀, a₁, ..., a_n-1, the symmetric sum is computed as follows:

\[ S = \sum_{i=0}^{\lfloor (n-1)/2 \rfloor} \Bigl(a_{i}+a_{n-1-i}\Bigr) \]

Note that if n is odd, the middle element is added only once. If the tree is empty (N = 0), simply output nothing.

Input Format: The first line contains an integer N, the number of values in the level order representation. The following line contains N space-separated integers denoting node values (-1 representing missing nodes).

Output Format: Print the symmetric sum for each level in one line, with each level's result separated by a single space.

inputFormat

The input is given via standard input (stdin) and includes:

• An integer N representing the number of values in the level order traversal.
• A sequence of N space-separated integers. The value -1 indicates that the corresponding child is missing.

outputFormat

Output the symmetric sum for each level of the binary tree in order, separated by a space. For an empty tree, output nothing.

7
1 2 3 -1 -1 4 5

1 5 9