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"
	"io"
	"os"
	"strconv"
)

var (
	readString func() string
	readBytes  func() []byte
)

func init() {
	readString, readBytes = newReadString(os.Stdin)
}

func newReadString(ior io.Reader) (func() string, func() []byte) {
	r := bufio.NewScanner(ior)
	r.Buffer(make([]byte, 1024), int(1e+11))
	r.Split(bufio.ScanWords)

	f1 := func() string {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Text()
	}
	f2 := func() []byte {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Bytes()
	}
	return f1, f2
}

func readInt() int {
	return int(readInt64())
}

func readInt64() int64 {
	i, err := strconv.ParseInt(readString(), 10, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

func readFloat64() float64 {
	f, err := strconv.ParseFloat(readString(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func minInt64(a, b int64) int64 {
	if a < b {
		return a
	}
	return b
}

func maxInt64(a, b int64) int64 {
	if a > b {
		return a
	}
	return b
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

func absInt64(a int64) int64 {
	if a < 0 {
		return -a
	}
	return a
}

func sum(a []int) int {
	var ret int
	for i := range a {
		ret += a[i]
	}
	return ret
}

func sumInt64(a []int64) int64 {
	var ret int64
	for i := range a {
		ret += a[i]
	}
	return ret
}

func sumFloat64(a []float64) float64 {
	var ret float64
	for i := range a {
		ret += a[i]
	}
	return ret
}

func gcdInt64(m, n int64) int64 {
	for m%n != 0 {
		m, n = n, m%n
	}
	return n
}

func lcmInt64(m, n int64) int64 {
	return m / gcdInt64(m, n) * n
}

// sort ------------------------------------------------------------

type int64Array []int64

func (s int64Array) Len() int           { return len(s) }
func (s int64Array) Swap(i, j int)      { s[i], s[j] = s[j], s[i] }
func (s int64Array) Less(i, j int) bool { return s[i] < s[j] }

type xxx struct {
	x int
}

type sortArray []xxx

func (s sortArray) Len() int           { return len(s) }
func (s sortArray) Swap(i, j int)      { s[i], s[j] = s[j], s[i] }
func (s sortArray) Less(i, j int) bool { return s[i].x < s[j].x }

// -----------------------------------------------------------------

func binarySearch(colors []int64, num int64) int {
	lo := 0
	hi := len(colors) - 1
	for lo < hi {
		mid := (lo + hi) / 2
		if colors[mid] <= num {
			lo = mid + 1
		} else {
			hi = mid
		}
	}
	return lo
}

func main() {
	n := readInt()
	a := make([]int64, n)
	for i := range a {
		a[n-1-i] = readInt64()
	}

	colors := make([]int64, 0, n)
	for i := range a {
		idx := binarySearch(colors, a[i])
		if len(colors) == 0 || colors[idx] <= a[i] {
			colors = append(colors, a[i])
		} else {
			colors[idx] = a[i]
		}
	}

	fmt.Println(len(colors))
}