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 Go (1.6) (judge verdict: Runtime Error)

package main

import "fmt"

const inf int = 1e9

func main() {
	var n int
	fmt.Scan(&n)
	as := make([]int, n)
	for i := 0; i < n; i++ {
		fmt.Scan(&as[i])
	}

	dp := make([]int, n)
	for i := 0; i < n; i++ {
		dp[i] = inf
	}

	for i := 0; i < n; i++ {
		a := as[n-i-1]
		k := upperBound(dp, a)
		dp[k] = a
	}

	ans := 0
	for i := 0; i < n; i++ {
		if dp[i] < inf {
			ans++
		}
	}

	fmt.Println(ans)
}

func upperBound(a []int, x int) int {
	lb, ub := -1, len(a)
	for ub-lb > 1 {
		m := (lb + ub) / 2
		if a[m] <= x {
			lb = m
		} else {
			ub = m
		}
	}
	return ub
}