Justin likes beans. In fact, he likes beans so much he wants to make a bean stew. There are ~N~ different bean species and Justin has ~c_n~ beans of the ~n^{th}~ species.

Justin's bean stew recipe requires ~d_n~ beans of the ~n^{th}~ species to make. Justin is very hungry, so help him find out how many bean stews he can possibly make!

Input Specification

The first line contains a single integer ~N~ ~(1\leq N\leq 10^5)~, the number of bean species.

The next line contains ~N~ space separated integers ~c_n~ ~(1\leq c_n\leq 10^8)~, where ~c_n~ represents how many beans of the ~n^{th}~ species Justin has.

The final line contains ~N~ space separated integers ~d_n~ ~(1\leq d_n\leq 10^8)~, where ~d_n~ represents how many beans of the ~n^{th}~ species is required by the bean stew recipe.

Output Specification

Output a single integer representing the total number of bean stews Justin can make.

Sample Input

3
7 10 2
2 4 1

Sample Output

2

Explanation for Sample Output

Making ~2~ bean stews takes ~4~ beans of the ~1^{st}~ species, ~8~ beans of the ~2^{nd}~ species and ~2~ beans of the ~3^{rd}~ species. Justin doesn't have enough ingredients to make any more stews after that.