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)

var input = require('fs').readFileSync('/dev/stdin', 'utf8');
var arr=input.trim().split("\n").map(Number);
var N=arr.shift();
var A=[];
var L=[];
for(var i=0;i<N;i++)A.push(arr.shift());
L[0] = A[0]
var length = 1;
for(var i=1;i<N;i++){
   if (L[length-1] < A[i])L[length++] = A[i];
   else {
      for(var j=0;j<length;j++){
         if(L[j]>=A[i]){L[j]=A[i];break;}
      }
   }
}
console.log(length);