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>) {
    val n = readLine()!!.toInt()

    val inputs = mutableListOf<Int>()
    for (i in 0 until n) {
        val a = readLine()!!.toInt()
        inputs.add(a)
    }

    // 数の順番の逆転数だけ色を塗ることになる

    var ans = 0

    var prev = inputs[1]
    for (i in 1 until n) {
        if(prev >= inputs[i]){
            ans += 1
        }

        prev = inputs[i]
    }
    if( ans == n-1) {
        println(n)
    } else {
        println(ans)
    }
}