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)

n = int(input())

cnt = 1

last = int(input())

buffer = [last]

for i in range(n - 1):
  a = int(input())
  # print(a, cnt)
  if a > last:
    last = a
  else:
    if len(buffer) == 0:
      buffer.append(last)
      cnt += 1
    if len(buffer) != 0:
      if a > buffer[-1]:
        last = a
        buffer.pop()
      else:
        cnt += 1
        last = a
        
print(cnt)