BMI Sorting

Problem Description

A person's Body Mass Index (BMI) equals their weight (in kilograms) divided by the square of their height (in meters).

For example, a person weighing $50\text{ kg}$ with a height of $1.6\text{ m}$ has a BMI of $50\text{ kg} / 1.6\text{ m} / 1.6\text{ m} = 19.53125\text{ kg/m}^2$.

There are now $n$ children; the $i$-th child has id $i$, weight $w_i$, and height $h_i$.

Sort the children by BMI from highest to lowest. The data guarantees that no two children have exactly the same BMI. Output the ids of the children after sorting.

Input Format

The input has $3$ lines:

• The first line is a positive integer $n$, the number of children;
• The second line contains $n$ integers $w_1, w_2, \dots, w_n$, the children's weights in $\text{kg}$;
• The third line contains $n$ floating-point numbers $h_1, h_2, \dots, h_n$, the children's heights in $\text{m}$.

Output Format

Output one line containing $n$ numbers: the ids of the children sorted by BMI from highest to lowest.

Sample Input

3
45 33 39
1.55 1.33 1.44

Sample Output

3 1 2

Sample Explanation

The three children (with ids $1$, $2$, $3$ in order) have BMIs (rounded to two decimal places) of $18.73$, $18.66$, $18.81$ respectively, so after sorting the output ids are $3$, $1$, $2$.

Constraints

$1 \le n \le 1000$, $10 \le w_i \le 100$, $0.8 \le h_i \le 1.9$, and each $h_i$ has exactly two decimal places.