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 (1.0.0) (judge verdict: Accepted)

import java.io.BufferedReader
import java.io.InputStreamReader
import java.io.PrintWriter
import java.util.*

fun main(args: Array<String>) = yorukatsu13e()

fun yorukatsu13e() = FastIO().exec {
    val n = int()
    val aList = (1..n).map { int() }

    val list = mutableListOf<Int>()

    fun lowerBound(list: List<Int>, key: Int): Int {
        var ok = list.size
        var ng = -1

        while (ok - ng > 1) {
            val mid = (ng + ok) / 2
            if (list[mid] >= key) ng = mid else ok = mid
        }
        return ok
    }

    for (a in aList) {
        val lowerBound = lowerBound(list, a)
        when (lowerBound) {
            in list.indices -> list[lowerBound] = a
            else -> list.add(a)
        }
    }

    val answer = list.size

    println(answer)
}

// region

@Suppress("unused")
class FastIO {
    private val br = BufferedReader(InputStreamReader(System.`in`))
    private var st = StringTokenizer("")
    val pw = PrintWriter(System.out)

    fun string(): String {
        if (!st.hasMoreTokens()) st = StringTokenizer(br.readLine())
        return st.nextToken()
    }

    fun int() = string().toInt()
    fun long() = string().toInt()
    fun double() = string().toInt()
    fun nextLine() = br.readLine()!!
    fun println() = pw.println()
    fun <T> print(o: T) = pw.print(o)
    fun <T> println(o: T) = pw.println(o)

    inline fun exec(code: FastIO.() -> Unit) {
        code()
        pw.flush()
    }
}
// endregion