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 Python3 (judge verdict: Accepted)

from bisect import bisect_left
import sys
input = sys.stdin.readline
def LIS():
    N = int(input())
    INF = 10000000000
    dp = [INF] * (N+1)
    for _ in range(N):
        x = int(input())
        dp[bisect_left(dp, x)] = x
    print(bisect_left(dp, INF - 1))

LIS()