Recursive analysis of a binary tree with memoization

Swift Hard functions

Task «Recursive analysis of a binary tree with memoization»

Write a function that takes a binary tree represented as an array of integers (level-order traversal, null is denoted as 0) and returns the maximum sum of node values from the root to a leaf, provided that no more than two consecutive nodes on the path can be skipped. Use a recursive function with memoization for efficient computation. The tree contains up to 1000 nodes, values range from -100 to 100.

Input Format

First line: an integer n (1 ≤ n ≤ 1000) — the number of elements in the array. Second line: n integers separated by spaces — the level-order representation of the tree (0 denotes the absence of a node).

Output Format

One integer — the maximum sum from the root to a leaf, considering the possibility of skipping no more than two consecutive nodes.

Examples

Example 1

INPUT

3
ab
bc
ca

OUTPUT

6

Example 2

INPUT

1
10

OUTPUT

10

Example 3

INPUT

5
10 5 15 0 0

OUTPUT

25

Example 4

INPUT

2
abc
def

OUTPUT

0

main.swift