Problem:
Score : 500 points

Problem Statement

You are given a sequence with N integers: A = \{ A_1, A_2, \cdots, A_N \}.
For each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

If A_i and A_j (i < j) are painted with the same color, A_i < A_j.

Find the minimum number of colors required to satisfy the condition.

Constraints

1 \leq N \leq 10^5

0 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the minimum number of colors required to satisfy the condition.

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

We can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1, 4, and 5 blue.

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)

N = int(input())
A = [int(input()) for _ in range(N)]
_A = [-a for a in A]

def LIS(seq):
    import bisect
    dp = [seq[0]]
    for s in seq[1:]:
        if s >= dp[-1]:
            dp.append(s)
        else:
            dp[bisect.bisect_right(dp,s)] = s
    return len(dp)
assert(LIS([2,2,1,4,1,5,1,1,1])==5)

print(LIS(_A))