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F. Heaps
time limit per test
2.5 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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 dpk(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 ≤ 3·105).

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.

Examples
Input
4
1 3
2 3
4 3
Output
21
Input
4
1 2
2 3
3 4
Output
22
Note

Consider sample case one.

For k ≥ 3 all dpk will be equal to 1.

For k = 2 dpk is 2 if and 1 otherwise.

For k = 1 dpk values are (3, 1, 2, 1) respectively.

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