Unfortunately, it turns out that a lot of the shows you've been watching this season haven't really lived up to their hype. To vent your frustration, you've decided to spend the weekend jumping in a tree instead.

The tree you're jumping in is rooted at node $1$ with $N$ nodes connected by $N-1$ edges, the $i$-th edge connecting nodes $u_i$ and $v_i$ with a length of $l_i$. Each node $i$ has $2$ values $r_i$ and $c_i$.

You may jump from node $a$ to node $b$ if $b$ is a descendant of $a$ and $r_a>c_b$, with a danger factor of ${\displaystyle \frac{dist(a,b)}{r_a-c_b}}$ where $dist(a,b)$ is the length of the shortest path from $a$ to $b$.

For each node $i$ from $2$ to $N$, find the minimum danger factor of a direct jump from some node to node $i$ or determine that it is impossible to jump to this node.

Constraints

$2\le N\le 3\times {10}^5$

$1\le r_i,c_i,l_i\le {10}^9$

$1\le u_i,v_i\le N$

Subtask 1 [30%]

$u_i=i$ and $v_i=i+1$ for all $i$.

Subtask 2 [70%]

No additional constraints.

Input Specification

The first line contains an integer $N$.

The second line contains $N$ integers $r_i$ $(1\le i\le N)$.

The third line contains $N$ integers $c_i$ $(1\le i\le N)$.

The next $N-1$ lines each contain $3$ integers $u_i$, $v_i$, and $l_i$.

Output Specification

Output $N-1$ lines, the $i$-th line containing the minimum danger factor of a direct jump from some node to node $i+1$ or Unreachable if it is impossible to jump to this node. Your output will be considered correct if the absolute or relative error of each numerical value does not exceed ${10}^{-9}$.

Sample Input

7
11 8 7 2 6 3 9
2 1 1 5 4 3 13
2 4 3
1 2 3
7 1 4
3 6 6
2 3 2
5 3 1

Sample Output

0.300000000000
0.285714285714
1.000000000000
0.333333333333
1.375000000000
Unreachable

Explanation

For node $2$, it is best to jump from node $1$ to node $2$ with a danger factor of ${\displaystyle \frac{3}{11-1}}={\displaystyle \frac{3}{10}}$.

For node $3$, it is best to jump from node $2$ to node $3$ with a danger factor of ${\displaystyle \frac{2}{8-1}}={\displaystyle \frac{2}{7}}$.

For node $4$, it is best to jump from node $1$ to node $4$ with a danger factor of ${\displaystyle \frac{6}{11-5}}=1$.

For node $5$, it is best to jump from node $3$ to node $5$ with a danger factor of ${\displaystyle \frac{1}{7-4}}={\displaystyle \frac{1}{3}}$.

For node $6$, it is best to jump from node $1$ to node $6$ with a danger factor of ${\displaystyle \frac{11}{11-3}}={\displaystyle \frac{11}{8}}$.

For node $7$, it is impossible to jump to this node.