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: Time Limit Exceeded)

package main

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

var si = bufio.NewScanner(os.Stdin)

const MAX = 1000000001

func readInt() int {
        si.Scan()
        ret, _ := strconv.Atoi(si.Text())
        return ret
}

func main() {
        si.Split(bufio.ScanWords)
        N := readInt()
        A := make([]int, N, N)
        for i := range A {
                A[i] = readInt()
        }
        dp := make([]int, 1, N+1)
        dp[0] = A[N-1]
        for i := N - 2; i >= 0; i-- {
                t := sort.Search(len(dp), func(j int) bool { return dp[j] > A[i] })
                if len(dp) > t && dp[t] > A[i] {
                        dp[t] = A[i]
                } else {
                        dp = append(dp, A[i])
                }
                sort.Ints(dp)
        }
        fmt.Println(len(dp))

}