Construct a Full Binary Tree from a Sequence

You are given a sequence of n integers. Your task is to determine whether you can construct a full binary tree (i.e. every non-leaf node has exactly two children) using the given sequence when interpreted as a level-order traversal. Note that a full binary tree must have an odd number of nodes. In this problem, the binary tree is formed as a complete binary tree: for a node at index i (0-indexed), its left child is at index 2i+1 and its right child is at index 2i+2. If a child index goes out of bounds, that child is considered nonexistent and represented by -1.

More formally, given a sequence (b_0, b_1, \dots, b_{n-1}), if (n) is even, output "NO" because a full binary tree must satisfy (n = 2k+1) for some non-negative integer (k). Otherwise, construct the tree and compute its depth (the number of edges in the longest path from the root to a leaf). Then output:

1. "YES" on the first line if the tree can be constructed.
2. The depth of the tree on the second line.
3. For each of the n nodes (in the same order as given in the input), output a line with three integers: the node value, the index of its left child, and the index of its right child (if a child does not exist, output -1).

If the tree cannot be constructed (i.e. n is even), simply output "NO".

Formula reminder: A full binary tree with (I) internal nodes has (2I+1) total nodes, i.e., (n=2I+1). ((n) must be odd.)

inputFormat

The first line contains an integer n, representing the number of nodes. The second line contains n space-separated integers denoting the sequence of node values.

outputFormat

If it is impossible to construct a full binary tree (i.e. if n is even), output a single line with the text "NO". Otherwise, output:

• The first line: "YES"
• The second line: an integer representing the depth of the tree
• The next n lines: each line contains three space-separated integers: the node value, the index of its left child, and the index of its right child (use -1 if the child does not exist)## sample

3
2 3 1

YES
1
2 1 2
3 -1 -1
1 -1 -1