The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Codeforces Round 172 (Div. 1) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

implementation

math

probabilities

trees

*2200

No tag edit access

The problem statement has recently been changed. View the changes.

×
C. Game on Tree

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMomiji has got a rooted tree, consisting of *n* nodes. The tree nodes are numbered by integers from 1 to *n*. The root has number 1. Momiji decided to play a game on this tree.

The game consists of several steps. On each step, Momiji chooses one of the remaining tree nodes (let's denote it by *v*) and removes all the subtree nodes with the root in node *v* from the tree. Node *v* gets deleted as well. The game finishes when the tree has no nodes left. In other words, the game finishes after the step that chooses the node number 1.

Each time Momiji chooses a new node uniformly among all the remaining nodes. Your task is to find the expectation of the number of steps in the described game.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 10^{5}) — the number of nodes in the tree. The next *n* - 1 lines contain the tree edges. The *i*-th line contains integers *a*_{i}, *b*_{i} (1 ≤ *a*_{i}, *b*_{i} ≤ *n*; *a*_{i} ≠ *b*_{i}) — the numbers of the nodes that are connected by the *i*-th edge.

It is guaranteed that the given graph is a tree.

Output

Print a single real number — the expectation of the number of steps in the described game.

The answer will be considered correct if the absolute or relative error doesn't exceed 10^{ - 6}.

Examples

Input

2

1 2

Output

1.50000000000000000000

Input

3

1 2

1 3

Output

2.00000000000000000000

Note

In the first sample, there are two cases. One is directly remove the root and another is remove the root after one step. Thus the expected steps are:

In the second sample, things get more complex. There are two cases that reduce to the first sample, and one case cleaned at once. Thus the expected steps are:

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/15/2024 19:27:55 (f1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|