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?
Input
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 $v$.
Output
For each testcase, if there exist a Hamiltonian path print "YES" , otherwise print "NO".
Sample Input
4
1 1
1 2
2 3
2 4
3
1 2
2 3
3 1
Sample Output
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).
