Uniform Rows After Column Flips

Medium

A light board is a grid grid of m rows and n columns: 1 means the bulb is on, 0 means it is off. Each column has its own switch that toggles every bulb in that column. You may press any switches, each as many times as you like. A row is uniform when its bulbs are all on or all off. Return the largest number of uniform rows you can get.

Example 1

grid=[[1, 0, 1], [0, 1, 0], [1, 1, 1]] → 2

Flip the middle column: the rows become [1, 1, 1], [0, 0, 0] and [1, 0, 1], so two are uniform.

Example 2

grid=[[0, 1], [0, 0]] → 1

The rows are neither equal nor opposite, so only one of them can be made uniform.

Example 3

grid=[[1, 0, 0, 1], [0, 1, 1, 0], [1, 0, 0, 1]] → 3

Flip columns 1 and 2: all three rows become uniform.

Constraints

1 ≤ m, n ≤ 300
grid[i][j] is 0 or 1

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Topics

Array Hash Table Matrix

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Input

grid=[[1, 0, 1], [0, 1, 0], [1, 1, 1]]

Expected

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