Problem Description

Given the complete bipartite graph. Each part of this graph has N vertices, i.e. the graph is balanced. An integer number (called a weight) assigns to each vertex. The weight of the edge is defined as the product of weights of vertices which connected by this edge.
It is well known, a matching in a graph is a set of edges without common vertices. A matching is perfect, if it covers all vertices of a graph.
Write a program to find a perfect match of the given bipartite graph with the maximal weight of the matching edges minimal.

Input

The input consists of multiple cases.
For each testcase,there will be exactly three lines;
The first line contains one integer number N (1 ≤ N ≤ 10⁵). The second line consist of N integer numbers, not exceeded 10⁹ by absolute value. The i-th number in line denotes a weight of i-th vertex of first part of a graph. In the third line, weights of vertices of second part are presented.

Output

The answer specified above.

3
1 2 3
9 10 11

27