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


def solve(n, sx):
    # Minimum value of last element in len(i+1) increasing subsequence.
    tbl = [float('inf')]*n
    # 5 6 9 1 10

    for i in range(n):
        idx = bisect_left(tbl, sx[i])
        tbl[idx] = sx[i]
        # [5,inf,inf,inf]
        # .
        # .
        # [5,6,9,inf,inf]
        # [1,6,9,inf,inf,]
        # [1,6,9,10,inf,]

    return bisect_left(tbl, float('inf'))


if __name__ == '__main__':
    n = int(input())
    sx = []
    for _ in range(n):
        sx.append(int(input()))

    print(solve(n, sx))