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: Wrong Answer)

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

fun yorukatsu13e() {
    val n = readLine()!!.toInt()
    val aList = (1..n).map { readLine()!!.toInt() }

    val list = mutableListOf(aList.first())

    fun lowerBound(list: List<Int>, key: Int): Int {
        var ng = 0
        var ok = list.lastIndex

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

    for (a in aList.drop(1)) {
        if (a <= list.first()) {
            list.add(0, a)
        } else {
            list[lowerBound(list, a)] = a
        }
    }

    val answer = list.size

    println(answer)
}