Maximize Strength of Machines

There are n machines each equipped with m power units (m ≥ 2). The power of the jthunit in the i-thmachine is denoted as machine_power[i][j]. The strength of a machine is defined as the minimum power among all its power units. We want to maximize the sum of the strength of all possible machines. For this, we can perform a 3-step operation multiple times (possibly 0): Select a machine that has not yet been marked. Transfer any one power unit from the selected machine to any other machine. Mark the selected machine, and it cannot be chosen for further operations. However, a marked machine can still receive power units from other machines. Find the max sum of the strength of all machines. Note: Each machine can transfer at most one power unit during the entire process, only when it is unmarked. A machine can receive power units from multiple other machines, even after it has been marked. The operation can be performed multiple times, but only unmarked machines can be selected during each operation.

Constraints

TO-DO</cod

Example 1

Input:

n = 3
m = 2
machine_power = [[1,5],[4,3],[2,10]]

Output:

16

Explanation: The operation are as follows: Select machine 1 and transfer the unit with power 1 to machine 2. now machine powers are = [[5],[1,4,3],[2,10]] Select machine 3 and transfer the unit with power 2 to machine 2 now machine powers are = [[5],[1,2,4,3],[10]] The sum of strenght is min(5) + min(1,2,4,3) + min(10) = 16 Return 16.