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: Wrong Answer)

from collections import defaultdict
from bisect import bisect_left

N = int(input())
d = defaultdict(list)

for i in range(N):
    v = int(input())
    d[v].append(i)

keys = sorted(d.keys())
s = d[keys[0]]

for k in keys[1:]:
    used = set()
    for i in d[k]:
        j = bisect_left(s, i)
        if 0<j<len(s):
            if not j-1 in used:
                s[j-1] = i
            else:
                s = s[:j] + [i] + s[j:]
            used |= {j-1}
        elif j==0:
            s = [i]+s
        else:
            s = s+[i]

print(len(s))