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 .

Input

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

Output the answer to the task.

Note

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, $4·1 + 4·1 + 2·2 + 2·1 + 3 + 1 + 2 + 1 = 21$.