Q : Given N containers, each container has balls of different colors, and each color can have multiple quantity in a single container. We need to select A quantity of color C1 , B quantity of color C2, C quantity of color C3 etc.

Penalty is equal to sum of all leftover quantity in a container if something is picked from container, else 0. We need to minimise the penalty and find set of containers which can help acheive minimum penalty.

Example

container 1 — [ (c1, 100), (c2, 100), (c3, 50) ] container 2 — [ (c1, 50), (c2, 50), (c3, 50) ] container 3 — [ (c1, 50), (c2, 50), (c3, 80) ]

we need to pick (c1, 100), (c2, 100)

1. If we select container 1 -> penalty = 50

2. If we select container (2,3) -> penalty = (50+80) = 130

So answer would be 50 and set of boxes would be [Container 1]

Constraints :

Container Count <= 100, Color Count <= 1000, Max quantity of each color <= 500

Time Limit : 60 seconds