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 ~\dfrac{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 ~\dfrac{3}{11-1} = \dfrac{3}{10}~.

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

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

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

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

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