The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
D. Bubble Sort Graph

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIahub 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.

Input

The first line of the input contains an integer *n* (2 ≤ *n* ≤ 10^{5}). The next line contains *n* distinct integers *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ *n*).

Output

Output a single integer — the answer to the problem.

Examples

Input

3

3 1 2

Output

2

Note

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].

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/24/2022 06:47:33 (i2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|