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 JavaScript (judge verdict: Accepted)

function Main(input) {
    input = input.trim().split("\n").map(function(x) { return x.split(" ")});

    const lowerBound = (arr, n) => {
        let first = 0, last = arr.length - 1, middle;
        while (first <= last) {
            middle = Math.floor((first + last) / 2);
            if (arr[middle] < n) first = middle + 1;
            else last = middle - 1;
        }
        return first;
    }


    let n = parseInt(input[0][0], 10);
    let v_a = [];
    for (let i = 0; i < n; i++){
        v_a.push(parseInt(input[i + 1][0], 10));
    }
    let dp = Array.from({length: n}, () => Infinity);

    dp[0] = v_a[0];
    let index;
    for (let i = 1; i < n; i++){
        index = lowerBound(dp, v_a[i]);
        dp[index] = v_a[i];
    }

    console.log(lowerBound(dp,1e9+1));

}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));