Input is a sorted array a[1 : n] of arbitrary real numbers. The array could only be of one of the following two types: 1) Type I: All the elements in the array are distinct; or 2) Type II: The array has √ n copies of one element, the other elements being distinct. Present a Monte Carlo algorithm that determines the type of the array in O( √ n log n) time. Show that the output of your algorithm will be correct with high probability.(Fact: (1 − x) 1/x ≤ 1/e for any 1 > x > 0.)