Two Lists - Pairwise Products and Square Root of the Sum (Hai danh sách - tích tương ứng và căn tổng)

Source: Problem Solving and Program Design in C

Version: Phuoc Hung OJ Extended

Problem

Given two non-negative integer sequences

$$x_0,x_1,\ldots,x_{n-1}\quad\text{and}\quad y_0,y_1,\ldots,y_{n-1},$$

define

$$z_i=x_i y_i,$$

and

$$S=\sum_{i=0}^{n-1}z_i,\qquad R=\sqrt{S}.$$

For every index, print $x_i,y_i,z_i$, then print $R$ with exactly $6$ digits after the decimal point.

Input

The first line contains $n$. The second line contains $x_i$. The third line contains $y_i$.

Output

For each $i$, print x_i y_i z_i on its own line. On the last line, print $R$ with exactly 6 digits after the decimal point.

Subtask

Subtask 1 (20 points): $1\le n\le5$, $0\le x_i,y_i\le100$.

Subtask 2 (30 points): $1\le n\le10$, $0\le x_i,y_i\le10^4$.

Subtask 3 (50 points): $1\le n\le20$, $0\le x_i,y_i\le10^6$.

Example

Input

4
1 2 3 4
5 6 7 8

Output

1 5 5
2 6 12
3 7 21
4 8 32
8.366600

Explanation

The sample follows the definitions and rules above.