A group of two or more people wants to meet and minimize the total travel distance. You are given a 2D grid of values 0 or 1, where each 1 marks the home of someone in the group. The distance is calculated usingManhattan Distance, where distance(p1, p2) =|p2.x - p1.x| + |p2.y - p1.y|.

Example:

Input:


1 - 0 - 0 - 0 - 1
|   |   |   |   |
0 - 0 - 0 - 0 - 0
|   |   |   |   |
0 - 0 - 1 - 0 - 0


Output: 6 

Explanation: 
Given three people living at 
(0,0)
, 
(0,4)
, and 
(2,2)
:
             The point 
(0,2)
 is an ideal meeting point, as the total travel distance 
             of 2+2+2=6 is minimal. So return 6.

class Solution {
    public int minTotalDistance(int[][] grid) {

        List<Integer> rows = collectRows(grid);
    List<Integer> cols = collectCols(grid);
    return minDistance1D(rows) + minDistance1D(cols);
    }

    private List<Integer> collectRows(int[][] grid){
        List<Integer> rows = new ArrayList<>();

        for (int row = 0; row < grid.length; row++){
            for (int col = 0; col < grid[0].length; col++){
                if (grid[row][col] == 1) rows.add(row);
            }
        }

        return rows;
    }

    private List<Integer> collectCols(int[][] grid){
        List<Integer> cols = new ArrayList<>();

        for (int col = 0; col < grid[0].length; col++){
            for (int row = 0; row < grid.length; row++){
                if (grid[row][col] == 1) cols.add(col);
            }
        }

        return cols;
    }

    private int minDistance1D(List<Integer> points) {
    int distance = 0;
    int i = 0;
    int j = points.size() - 1;
    while (i < j) {
        distance += points.get(j) - points.get(i);
        i++;
        j--;
    }
    return distance;
}
}