Let A = (a1, a2, ..., an) be a sequence of numbers. Another sequence Z = (z1, z2, ..., zm), m<= n is a subsequence of A if there exists a strictly increasing sequence (i1, i2, ..., ik) of indices of A such that for all j = 1, 2, ..., k, zj = Aij . More intuitively, the sequence Z is obtained by deleting some numbers from A without changing the order of the remaining numbers. For example, if A = (1, 3, 5, 7, 9, 11), then Z = (3, 9, 11) is a subsequence of A. Design an O(n^2) dynamic programming algorithm to find the longest mononotincally increasing subseqquence of a sequence of n numbers