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: Time Limit Exceeded)

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val aa = IntArray(n) { readLine()!!.toInt() }
    val palette = mutableListOf<Int>()
    var color = 0
    palette.add(aa[0])
    repeat(n - 1) {
        val a1 = aa[it]
        val a2 = aa[it + 1]
        if (a1 < a2) {
            palette[color] = a2
            return@repeat
        }
        palette.forEachIndexed { i, c ->
            if (i == color) return@forEachIndexed
            if (c < a2) {
                color = i
                palette[color] = a2
                return@repeat
            }
        }
        palette.add(a2)
        color = palette.size - 1
    }
    println(palette.size)
}