Good Binary Tree Verification

You are given a binary tree where each node is represented by a triplet of integers (value, left, right). A value of -1 indicates a missing child. The tree is considered good if for every level of the tree, the sequence of node values (traversed from left to right) is strictly increasing. In other words, if a level has nodes with values \(a_1, a_2, \dots, a_k\), then the condition

\(a_1 < a_2 < \dots < a_k\)

must hold. If the tree is empty, it is considered good.

inputFormat

The input is read from stdin and has the following format:

• The first line contains an integer n which is the number of nodes in the tree. If n = 0, the tree is empty.
• If n > 0, the following n lines each contain three space-separated integers: value, left, and right. Here, left and right are the values of the left and right children respectively, with -1 indicating a missing child.

outputFormat

Output a single line to stdout containing either YES if the binary tree is good or NO otherwise.

6
10 5 15
5 3 6
15 -1 20
3 -1 -1
6 -1 -1
20 -1 -1

YES