RU-SPB 2020 Problem 94

On a table with $25$ columns and $300$ rows, Kostya painted all its cells in three colors. Then, Lesha, looking at the table, for each row names one of the three colors and marks in that row all cells of that color (if there are no cells of that color in that row, he does nothing). After that, all columns that have at least a marked square will be deleted. Kostya wants to be left as few as possible columns in the table, and Lesha wants there to be as many as possible columns in the table. What is the largest number of columns Lesha can guarantee to leave?