Problem:
Longest Increasing Subsequence

For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.

An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.

Input

n
a0
a1
:
an-1

In the first line, an integer n is given. In the next n lines, elements of A are given.

Output

The length of the longest increasing subsequence of A.

Constraints

1 ≤ n ≤ 100000

0 ≤ ai ≤ 109

Sample Input 1

5
5
1
3
2
4

Sample Output 1

3

Sample Input 2

3
1
1
1

Sample Output 2

1

Solution in Go (judge verdict: Accepted)

package main

import (
	"fmt"
	"sort"
)

var n int

func main() {
	fmt.Scan(&n)

	var arr []int
	for i := 0; i < n; i++ {
		var a int
		fmt.Scan(&a)
		arr = append(arr, a)
	}

	var lis []int
	lis = append(lis, arr[0])
	for i := 1; i < len(arr); i++ {
		if val, last := arr[i], lis[len(lis)-1]; val == last {
		} else if last < val {
			lis = append(lis, val)
		} else {
			f := func(j int) bool {
				return val < lis[j]
			}
			index := sort.Search(len(lis), f)
			if index == 0 || lis[index-1] != val {
				lis[index] = val
			}
		}
	}
	fmt.Println(len(lis))
}