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: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"io"
	"os"
	"strconv"
	"strings"
)

type Color struct {
	MaxNumber int
	Color int
}

func calc(arr []int, times int)  {
	colorArr := make([]Color,0)
	lastColor := new(Color)
	for i := 0; i < len(arr); i ++ {
		isCheck := true
		if i > 0 && arr[i] > arr[i-1] {
			lastColor.MaxNumber = arr[i]
			continue
		}
		for j := 0; j < len(colorArr); j++ {
			if colorArr[j].MaxNumber < arr[i]{
				colorArr[j].MaxNumber = arr[i]
				isCheck = false
				*lastColor = colorArr[j]
				break
			}
		}
		if isCheck {
			colorS := new(Color)
			colorS.MaxNumber = arr[i]
			colorArr = append(colorArr, *colorS)
			*lastColor = *colorS
		}
	}
	fmt.Println(len(colorArr))
}

func main() {
	arr := make([]int,0)
	reader := bufio.NewReaderSize(os.Stdin, 1024*1024)
	times, _:= strconv.Atoi(readLine(reader))
	for i:= 0; i< times; i++ {
		tmp, _ := strconv.Atoi(readLine(reader))
		arr = append(arr, tmp)
	}
	calc(arr, times)
}

func readLine(reader *bufio.Reader) string {
	str, _, err := reader.ReadLine()
	if err == io.EOF {
		return ""
	}

	return strings.TrimRight(string(str), "\r\n")
}