A11755. Heaps

You're given a tree with $n$ vertices rooted at $1$ .

We say that there's a $k$ -ary heap of depth $m$ located at $u$ if the following holds:

- For $m=1$ $u$ itself is a $k$ -ary heap of depth $1$ .
- For $m>1$ vertex $u$ is a $k$ -ary heap of depth $m$ if at least $k$ of its children are $k$ -ary heaps of depth at least $m-1$ .

Denote $dp_{k}(u)$ as maximum depth of $k$ -ary heap in the subtree of $u$ (including $u$ ). Your goal is to compute .

The first line contains an integer $n$ denoting the size of the tree $(2<=n<=3·10^{5})$ .

The next $n-1$ lines contain two integers $u$ , $v$ each, describing vertices connected by $i$ -th edge.

It's guaranteed that the given configuration forms a tree.

Output the answer to the task.

Consider sample case one.

For $k>=3$ all $dp_{k}$ will be equal to $1$ .

For $k=2$ $dp_{k}$ is $2$ if  and $1$ otherwise.

For $k=1$ $dp_{k}$ values are $(3,1,2,1)$ respectively.

To sum up, $4·1+4·1+2·2+2·1+3+1+2+1=21$ .