Rikka with Tree

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:

For a tree $T$, let $F(T,i)$ be the distance between vertice 1 and vertice $i$.(The length of each edge is 1).

Two trees $A$ and $B$ are similiar if and only if the have same number of vertices and for each $i$ meet $F(A,i)=F(B,i)$.

Two trees $A$ and $B$ are different if and only if they have different numbers of vertices or there exist an number $i$ which vertice $i$ have different fathers in tree $A$ and tree $B$ when vertice 1 is root.

Tree $A$ is special if and only if there doesn't exist an tree $B$ which $A$ and $B$ are different and $A$ and $B$ are similiar.

Now he wants to know if a tree is special.

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 $n-1$ 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 the tree is special print "YES" , otherwise print "NO".

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

YES
NO

For the second testcase, this tree is similiar with the given tree:
4
1 2
1 4
3 4

BestCoder Round #53 (div.2)