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"
	"os"
	"strconv"
)

var scanner = bufio.NewScanner(os.Stdin)

func next() string {
	scanner.Scan()
	return scanner.Text()
}

func nextInt() int {
	i, _ := strconv.Atoi(next())
	return i
}

func main() {
	scanner.Split(bufio.ScanWords)

	n := nextInt()
	colors := make([]int, 1)
	colors[0] = 0
	largestNum := -1
	colorIndex := 0

	for i := 0; i < n; i++ {
		num := nextInt()
		if num > largestNum {
			largestNum = num
		} else {
			colors[colorIndex] = largestNum

			largestIndex := -1
			largestValue := -1
			for i, v := range colors {
				if num > v && v > largestValue {
					largestIndex = i
					largestValue = v
				}
			}

			if largestIndex != -1 {
				largestNum = num
				colorIndex = largestIndex
			} else {
				largestNum = num
				colors = append(colors, num)
				colorIndex = len(colors) - 1
			}
		}
	}

	fmt.Println(len(colors))
}