Leo the fox has a 5 by 5 checkerboard grid with alternating red and black squares. He fills in the grid with the numbers 1, 2, 3, . . . , 25 such that any two consecutive numbers are in adjacent squares (sharing a side) and each number is used exactly once. He then computes the sum of the numbers in the 13 squares that are the same color as the center square. Compute the maximum possible sum Leo can obtain.

Source: Combinatorics Round, HMMT (Harvard-MIT Math Tournament) Spring 2021

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