Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a 1 , a 2 , ..., a n in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G ) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode). procedure bubbleSortGraph() build a graph G with n vertices and 0 edges repeat swapped = false for i = 1 to n - 1 inclusive do: if a[i] a[i + 1] then add an undirected edge in G between a[i] and a[i + 1] swap( a[i], a[i + 1] ) swapped = true end if end for until not swapped * repeat the algorithm as long as swapped value is true. * end procedure For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G , if we use such permutation as the premutation a in procedure bubbleSortGraph.

输入描述:

The first line of the input contains an integer n (2 ≤ n ≤ 105). The next line contains n distinct integers a1, a2, ..., an(1 ≤ ai ≤ n).

输出描述:

Output a single integer — the answer to the problem.

备注:

Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].