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: Time Limit Exceeded)

#最長増加部分列問題 (LIS) 
import bisect

N = int(input())
seq = [0] * N
for i in range(N):
  seq[i] = int(input())

LIS = [seq[0]]
#print(LIS)
for i in range(1, len(seq)):
    if seq[i] <= LIS[0]:
        LIS.insert(0, seq[i])
    else:
        LIS[bisect.bisect_left(LIS, seq[i]) - 1] = seq[i]
    #print(LIS)
#print(LIS)
print(len(LIS))