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 (
	"fmt"
	)

	
func main() {
	var n int
	fmt.Scan(&n)
	m:=[]int{}
	c:=[]int{}
	
	for i:=0;i<n;i++{
		var ai int
		fmt.Scan(&ai)
		m=append(m,ai)
	}
	
	c = append(c, m[0])
	for i:=1;i<n;i++{
		addc := false
		for j:=0;j<len(c);j++{
			if m[i] <= c[j] {
				addc = true
			} else {
				addc = false 
			}
		}
		if addc {
			c = append(c,m[i])
		}
	}

	fmt.Println(len(c))
}