github.com/captn3m0/codechef.git

---
category_name: easy
problem_code: TREE3
problem_name: 'Triple-tree decomposition'
languages_supported:
    - C
    - CPP14
    - JAVA
    - PYTH
    - 'PYTH 3.5'
    - PYPY
    - CS2
    - 'PAS fpc'
    - 'PAS gpc'
    - RUBY
    - PHP
    - GO
    - NODEJS
    - HASK
    - rust
    - SCALA
    - swift
    - D
    - PERL
    - FORT
    - WSPC
    - ADA
    - CAML
    - ICK
    - BF
    - ASM
    - CLPS
    - PRLG
    - ICON
    - 'SCM qobi'
    - PIKE
    - ST
    - NICE
    - LUA
    - BASH
    - NEM
    - 'LISP sbcl'
    - 'LISP clisp'
    - 'SCM guile'
    - JS
    - ERL
    - TCL
    - kotlin
    - PERL6
    - TEXT
    - 'SCM chicken'
    - CLOJ
    - COB
    - FS
max_timelimit: '1'
source_sizelimit: '50000'
problem_author: altruist_
problem_tester: kingofnumbers
date_added: 20-04-2018
tags:
    - altruist_
editorial_url: 'https://discuss.codechef.com/problems/TREE3'
time:
    view_start_date: 1524934802
    submit_start_date: 1524934802
    visible_start_date: 1524934802
    end_date: 1735669800
    current: 1525198943
is_direct_submittable: false
layout: problem
---
All submissions for this problem are available.### Read problems statements in [Mandarin chinese](http://www.codechef.com/download/translated/LTIME59/mandarin/TREE3.pdf), [Russian](http://www.codechef.com/download/translated/LTIME59/russian/TREE3.pdf) and [Vietnamese](http://www.codechef.com/download/translated/LTIME59/vietnamese/TREE3.pdf) as well.

Kefaa has developed a novel decomposition of a tree. He claims that this decomposition solves many difficult problems related to trees. However, he doesn't know how to find it quickly, so he asks you to help him. You are given a tree with $N$ vertices numbered $1$ through $N$. Let's denote an edge between vertices $u$ and $v$ by $(u, v)$. The \*triple-tree decomposition\* is a partition of edges of the tree into unordered triples of edges $(a, b), (a, c), (a, d)$ such that $a \\neq b \\neq c \\neq d$. Each edge must belong to \*\*exactly one\*\* triple. Help Kefaa with this problem — find a triple-tree decomposition of the given tree or determine that no such decomposition exists. ### Input - The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows. - The first line of each test case contains a single integer $N$. - Each of the following $N-1$ lines contains two space-separated integers $u$ and $v$ describing an edge between vertices $u$ and $v$ of the tree. ### Output - For each test case, print a line containing the string `"YES"` if a triple-tree decomposition of the given tree exists or `"NO"` otherwise. - If it exists, print $\\frac{N-1}{3}$ more lines describing a decomposition. - Each of these lines should contain four space-separated integers $a$, $b$, $c$ and $d$ describing a triple of edges $(a, b), (a, c), (a, d)$. If more than one triple-tree decomposition exists, you may output any one. ### Constraints - $1 \\le T \\le 100$ - $2 \\le N \\le 2 \\cdot 10^5$ - $1 \\le u, v \\le N$ - the sum of $N$ over all test cases does not exceed $2 \\cdot 10^5$ ### Subtasks \*\*Subtask #1 (20 points):\*\* $2 \\le N \\le 10$ \*\*Subtask #2 (30 points):\*\* $2 \\le N \\le 5000$ and the sum of $N$ overall testcases doesn't exceed $5000$ \*\*Subtask #3 (50 points):\*\* original constraints ### Example Input ``` 2 4 1 2 1 3 1 4 7 1 2 2 3 1 4 4 5 1 6 6 7 ``` ### Example Output ``` YES 1 2 3 4 NO ```