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F. Heaps

time limit per test

2.5 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputYou'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.

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 *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.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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