Let i0, i1, . . . , in be a rearrangement of the integers 0, 1, . . . , n. Show that f [xi0 , xi1 , . . ., xin] = f [x0, x1, . . ., xn]. [Consider the leading coefficient of the nth Lagrange polynomial on the data {x0, x1, . . . , xn} = {xi0 , xi1 , . . . , xin}.]