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 Python (3.4.3) (judge verdict: Time Limit Exceeded)


import bisect

def solve(N, As):
    colors = []
    for a in As:
        if not colors:
            colors.append(a)
        else:
            if a <= colors[0]:
                colors.insert(0, a)
            else:
                i = bisect.bisect_left(colors, a)
                colors[i - 1] = a
                j = i - 1
                while j + 1 < len(colors) and colors[j] > colors[j + 1]:
                    colors[j], colors[j + 1] = colors[j + 1], colors[j]
                    j += 1
        # print(colors)
    return len(colors)



if __name__ == "__main__":
    N = int(input())
    As = []
    [As.append(int(input())) for i in range(N)]
    print(solve(N, As))