B'Mr. Chanek gives you a sequence a indexed from 1 to n . Define f(a) as the number of indices where a_i = i . You can pick an element from the current sequence and remove it, then concatenate the remaining elements together. For example, if you remove the 3 -rd element from the sequence [4, 2, 3, 1] , the resulting sequence will be [4, 2, 1] . You want to remove some elements from a in order to maximize f(a) , using zero or more operations. Find the largest possible f(a) . The first line contains one integer n ( 1 <= q n <= q 2 cdot 10^5 ) -- the initial length of the sequence. The second line contains n integers a_1, a_2, ldots, a_n ( 1 <= q a_i <= q 2 cdot 10^5 ) -- the initial sequence a . Output an integer denoting the largest f(a) that can be obtained by doing zero or more operations. In the first example, f(A) = 3 by doing the following operations. [2,1, textbf{4},2,5,3,7] rightarrow [ textbf{2},1,2,5,3,7] rightarrow [1,2,5,3, textbf{7}] rightarrow [1,2, textbf{5},3] rightarrow [1,2,3] In the second example, f(A) = 2 and no additional operation is needed. '...