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 sys
sys.setrecursionlimit(4100000)
input = sys.stdin.readline

from bisect import bisect_left

n = int(input())
a = int(input())

color = [a]
color_min = a

for _ in range(1, n):
    a = int(input())
    if color_min >= a:
        j = bisect_left(color, a)
        color.insert(j, a)
        color_min = a
    else:
        j = bisect_left(color, a)
        del color[j-1]
        j = bisect_left(color, a)
        color.insert(j, a)
        color_min = color[0]

print(len(color))