Let n ∈ Z+, n odd. If i1i2, . . . , in is a permutation of the integers 1, 2, ..., n, prove that (1 - i 1)(2 - i2) ∙ ∙ ∙ ∙ ∙ ∙ ∙ (n - in) is an even integer. (Which counting principle is at work here?)