Rikka with Graph II

As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:

Yuta has a non-direct graph with $n$ vertices and $n$ edges. Now he wants you to tell him if there exist a Hamiltonian path.

It is too difficult for Rikka. Can you help her?

There are no more than 100 testcases.

For each testcase, the first line contains a number $n(1 \leq n \leq 1000)$.

Then $n$ lines follow. Each line contains two numbers $u,v(1 \leq u,v \leq n)$ , which means there is an edge between $u$ and $v$.

For each testcase, if there exist a Hamiltonian path print "YES" , otherwise print "NO".

4
1 1
1 2
2 3
2 4
3
1 2
2 3
3 1

NO
YES

Hint
For the second testcase, One of the path is 1->2->3
If you doesn't know what is Hamiltonian path, click here (https://en.wikipedia.org/wiki/Hamiltonian_path).

BestCoder Round #53 (div.2)