Momiji 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 $10^{ - 6}$.

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:

$1 × (1 / 2) + 2 × (1 / 2) = 1.5$

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:

$1 × (1 / 3) + (1 + 1.5) × (2 / 3) = (1 / 3) + (5 / 3) = 2$