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)

def li():
    return list(map(int, input().split()))


if __name__ == "__main__":
    n = int(input())
    a_list = [int(input()) for _ in range(n)]

    color_list = []

    for a in a_list:
        # 既存の色でぬれるかチェック
        can_draw = False
        # 増分が一番小さいものを選ぶ
        best_diff = 10 ** 9 + 1
        best_index = -1
        for index, color in enumerate(color_list):
            if color < a:
                can_draw = True
                diff = a - color
                if diff < best_diff:
                    best_diff = diff
                    best_index = index
        if can_draw:
            color_list[best_index] = a
        else:
            color_list.append(a)
        # print(color_list)
    # print()
    # print(color_list)
    print(len(color_list))

# a1から順番に塗っていく
# 色ごとに、今まで塗った最大値を記録する
# 既存の色でぬれる場合は、なるべく最大値の増分が少なくなるように色を選ぶ
# 既存の色でぬれない場合は新しい色を作って最大値を記録する