Statement

Like every year, Luca is organizing the famous Exatlon Battle: a test of strength, skill and logic. As usual, the competitors will be split in two teams, The Famous (the red team) and The Warriors (the blue team). Luca's favorite test in the competition is as follows: each team receives a square formed by N boards of equal shape, but of different color. Each board has length N and width 1. The boards are formed by square cells of sizes 1 × 1, each of them being painted red or blue. For example, the following figure shows a board of length 6, where the first and the fourth zones are painted red, while the zones 2, 3, 4 and 6 are blue: The players can reorder the boards, but they cannot change the colors in each individual board. The goal of each player is to produce a rectangular zone of the maximum possible area, painted with the color of their team. The team which forms the largest rectangular area of their own color will win the match...