Burgers

Kai the lobster is starting a burger chain selling burgers. He has $n$ ingredients to work with, which are labelled from $1$ to $n$. For each ingredient $i$, he has $x\[i]$ portions of ingredient $i$.

He has two recipes for burgers. For each ingredient $i$, the first recipe requires $a\[i]$ portions of ingredient $i$ and the second recipe requires $b\[i]$ portions of ingredients $i$.

Can you help Kai compute the maximum total number of burgers he can make?

The first line of input consists of one integer $n$, the number of different ingredients.

The second line consists of $n$ spaced integers $x\[1], x\[2], \dots , x\[n - 1], x\[n]$, the total number of portions Kai has of each ingredient.

The third line consists of $n$ spaced integers $a\[1], a\[2], \dots , a\[n - 1], a\[n]$, the number of portions of each ingredient for the first recipe.

The fourth line consists of $n$ spaced integers $b\[1], b\[2], \dots , b\[n - 1], b\[n]$, the number of portions of each ingredient for the second recipe.

The output should contain a single integer on a single line, the largest number of burgers Kai can make.

• $1 ≤ n ≤ 100\\,000$
• $1 ≤ x\[i], a\[i], b\[i] ≤ 10^9$