Fewest changes to draw the letter Y in a grid

An n x n grid (n odd) holds only the values 0, 1 and 2. The letter Y is made of the two diagonals running from the top corners down to the centre, plus the centre column from the centre to the bottom. Every Y cell must end up holding one value and every other cell a different value. Return the fewest cells you must change. Count the values inside and outside the Y once, then try each ordered pair of distinct values.