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 $\text{[math]}$ .

Input

The first line contains an integer n denoting the size of the tree (2 ≤ n ≤ 3·10⁵).

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 $\text{[math]}$ 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.

Heaps