Rounds of Row Maximums

Medium

You are given a table grid whose rows all have the same length. The score starts at zero. While the table is not empty, play a round: 1. Remove the largest number from every row (if there are ties, any one of them). 2. Take the largest of the numbers removed this round and add it to the score. Return the final score.

Example 1

grid=[[4, 9, 1], [8, 2, 8]] → 19

Round 1 removes 9 and 8 and scores 9. Round 2 removes 4 and 8 and scores 8. Round 3 removes 1 and 2 and scores 2. Total 9 + 8 + 2 = 19.

Example 2

grid=[[3], [0], [5]] → 5

A single round takes 3, 0 and 5, scoring 5.

Constraints

1 ≤ len(grid) ≤ 300
1 ≤ len(grid[i]) ≤ 500, all rows have the same length
0 ≤ grid[i][j] ≤ 1000

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Topics

Array Matrix Sorting Simulation Heap (Priority Queue)

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Input

grid=[[4, 9, 1], [8, 2, 8]]

Expected

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