Problem:
Score : 500 points

Problem Statement

You are given a sequence with N integers: A = \{ A_1, A_2, \cdots, A_N \}.
For each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

If A_i and A_j (i < j) are painted with the same color, A_i < A_j.

Find the minimum number of colors required to satisfy the condition.

Constraints

1 \leq N \leq 10^5

0 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the minimum number of colors required to satisfy the condition.

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

We can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1, 4, and 5 blue.

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.

Solution in Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.PrintWriter
import java.util.*
import kotlin.collections.ArrayDeque

val br = System.`in`.bufferedReader()
val out = PrintWriter(System.out)

fun main() {
    br.use { out.use {
        solve()
        out.flush()
    } }
}

fun solve() {
    val n = readInteger()
    val aArray = IntArray(n) { readInteger() }

    // linkedListのほうが良さそう
    val colorDequeue = mutableListOf<Int>() // 使用した色に対して最後に塗った数値
    var ans = 1
    colorDequeue += aArray.first()
    for (a in aArray.drop(1)) {
        var left = -1
        var right = colorDequeue.size
        while (right - left > 1) {
            val mid = (right + left) / 2
            if (colorDequeue[mid] < a) left = mid else right = mid
        }

        if (left == -1) {
            ans++
            colorDequeue.add(0, a)
        } else {
            colorDequeue[left] = a
        }
    }
    out.println(ans)
}

fun readInteger() = Integer.parseInt(br.readLine())
fun readLong() = java.lang.Long.parseLong(br.readLine())
fun readStringList() = br.readLine()!!.split(' ')
fun readIntegerList() = readStringList().map(Integer::parseInt)
fun readLongList() = readStringList().map(java.lang.Long::parseLong)
fun readDoubleList() = readStringList().map(java.lang.Double::parseDouble)