Afifa's ITS

Imagine some made up story here including Afifa (my little sister) and an Intelligent Transport System, which ultimately leads to the main problem.

You are given a connected tree containing $N$ nodes and $N - 1$ bidirectional edges. That means, you can go from one node to any other node. Every node $i$ has some weight $w_i$. Let's keep it simple and say that $w_i = i$ for the $i$-th node. Let this tree be called A.

Let's call a node terminal if it has one edge attached to it or no edge at all.

You have to pick a "part" of this tree that's also a tree. You can pick the entire tree as well. Let this new tree be called B.

Fig - 1 denotes an example of tree $A$. Fig - 2 and fig - 3 shows two of the many possible ways to pick tree $B$. Now, you have to do this in a way so that the cost is maximum.

The cost of choosing tree $B = \text{(minimum weight among the terminals of B)} \times \text{(number of edges in B)}$.

For fig -2, the cost is $minimum(3, 4, 6) \times 3 = 9$ and for fig - 3, the cost is $minimum(1, 6) \times 4 = 4$. Neither of the costs are maximum.

Input

The first line contains a single integer $N$ ($1 ≤ N ≤ 100000$) - number of nodes in the tree. Each of the next $N - 1$ lines contains two integers $u$ and $v$ ($1 ≤ u, v ≤ N$) - denoting an edge of the tree.

Output

Print the maximum possible cost of new tree $B$.

Sample

Input	Output
7 2 4 1 2 2 5 3 7 4 7 6 7	20
Here, tree $B$, marked with bold edges, has two terminals with weight 5 and 6. Number of edges in $B$ equals 4. So the cost is $minimum(5, 6) \times 4 = 20$, which is the maximum possible cost for this case.