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: Wrong Answer)

N = int(input())
number_list = [int(input()) for _ in range(N)]

color_count = 0
num_prev = 10e10
color_list = []

for num in number_list:
	if num < num_prev:
		if color_list == []:
			color_count +=1
			color_list.append(num)
		else:
			same_color = False
			for idx, c_num in enumerate(color_list[::-1]):
				if c_num < num:
					color_list[-idx-1] = num      
					same_color = True
					break
          
			if not same_color:
				color_count +=1
				color_list.append(num)
	else:
		color_list[-1] = num
	num_prev = num

print(color_count)