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Solution: Valid Square

Explore how to determine if four points in 2D space form a square by calculating squared distances, checking side and diagonal equality, and applying geometric rules for efficient problem solving.

Statement

Given the coordinates of four points P1P_1, P2P_2, P3P_3, and P4P_4 in 2D space, determine if these points form a square.

Each point PiP_i is represented as [xi, yi][x_i,\space y_i] ...