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: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

var (
	sc = bufio.NewScanner(os.Stdin)
)

func init() {
	sc.Split(bufio.ScanWords)
}

func readInts(n int) []int {
	a := make([]int, n)
	for i := range a {
		sc.Scan()
		a[i], _ = strconv.Atoi(sc.Text())
	}
	return a
}

func main() {
	var n int
	fmt.Scan(&n)
	a := readInts(n)
	d := make([]int, 0, n)
	for _, e := range a {
		i := sort.Search(len(d), func(i int) bool { return d[i] < e })
		if i == len(d) {
			d = append(d, e)
		} else {
			d[i] = e
		}
	}
	fmt.Println(len(d))
}