Two Array Average

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.