Maximize the Minimum Sum

You are given two arrays A and B of length N. Your task is to choose a permutation P of indices for array B such that when you form a new array C by computing

\( C[i] = A[i] + B[P[i]] \) for \(0 \le i < N\),

the minimum element of C is as large as possible. In other words, you want to maximize \( \min(C) \).

Input format: The input consists of three lines. The first line is an integer N, which represents the number of elements in the arrays. The second line contains N space-separated integers representing the array A. The third line contains N space-separated integers representing the array B.

Output format: Output a single integer, the maximum possible value of \( \min(C) \) given the optimal permutation P.

Hint: A greedy strategy of sorting A in ascending order and B in descending order will yield the optimal result.

inputFormat

The first line contains an integer N.

The second line contains N space-separated integers, the elements of array A.

The third line contains N space-separated integers, the elements of array B.

outputFormat

Output a single integer: the maximum possible value of the minimum element of array C.

## sample

3
1 3 5
2 4 6

7

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