Define the gcd function for more than two arguments by the recursive equation gcd (a₀, a₁, . . . ,a_n) = gcd (a₀, gcd (a₁, a₂, . . . ,a_n). Show that the gcd function returns the same answer independent of the order in which its arguments are specified. Also show how to find integers x₀, x₁, . . . ,x_n such that gcd (a₀, a₁, . . . ,a_n) = a₀x₀ + a₁x₁ + ···+ a_nx_n. Show that the number of divisions performed by your algorithm is O(n + lg(max {a₀, a₁, . . . ,a_n})).