You are given two arrays of $n$ integers.

Your task is to select a nonempty prefix from both arrays such that the average of all selected numbers is as large as possible.

Input

The first line has an integer $n$.

The second line has $n$ integers $a_1,a_2,\dots,a_n$: the numbers in the first array.

The third line has $n$ integers $b_1,b_2,\dots,b_n$: the numbers in the second array.

Output

Print two numbers: the prefix sizes.

Your answer is considered correct if the absolute or relative difference to the maximum average is at most $10^{-6}$.

Constraints

• $1 \le n \le 10^5$
• $1 \le a_i, b_i \le 10^9$

Example

Input:

4
1 5 5 2
3 1 3 1

Output:

3 1

Explanation: if you choose the prefixes $[1,5,5]$ and $[3]$, the average is $(1+5+5+3)/4=3.5$ which is the maximum possible average.