Min Cost Connect Groups

Given a cost matrix connecting two groups of points, find the minimum total cost to connect every point in both groups such that each point connects to at least one point in the other group.

Examples
Input: [[1,2,3],[4,5,6],[7,8,9]]
Output: 6
Hints

Min Cost Connect Groups

Given a cost matrix connecting two groups of points, find the minimum total cost to connect every point in both groups such that each point connects to at least one point in the other group.