Problem Description

Lobster Kai runs a burger shop. Making one burger requires $n$ kinds of ingredients, and for the $i$-th ingredient he has $x_i$ portions.

He has two burger recipes. For the $i$-th ingredient, these two recipes require $a_i$ portions and $b_i$ portions respectively.

Compute the maximum number of burgers Kai can make with these ingredients.

Input Format

The first line contains a positive integer $n$.

The second line contains $n$ integers, representing $x$.

The third line contains $n$ integers, representing $a$.

The fourth line contains $n$ integers, representing $b$.

Output Format

Output one integer per line, representing the maximum number of burgers that can be made.

3
14 10 100
3 1 1
2 3 1

5

2
83 72
1 3
1 3

24

Hint

Sample #1 Explanation

Kai can make $3$ burgers of the first type and $2$ burgers of the second type.

Sample #2 Explanation

Kai can make $24$ burgers of the first type, or $24$ burgers of the second type.

Constraints

For $100\%$ of the testdata, $1 \le n \le 100000$, $1 \le x_i,a_i,b_i \le 10^9$.

Translated by ChatGPT 5