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Solution: Valid Square

Understand how to verify whether four points in 2D space form a valid square by using geometric properties. Learn to calculate squared distances between all point pairs, sort them, and check the equality of sides and diagonals to confirm the square's shape. This lesson helps you apply geometric reasoning with an efficient coding solution.

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] ...