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)

n = int(input())
alist = [int(input()) for _ in range(n)]
argsort = [i for i, v in sorted(enumerate(alist), key=lambda x: x[1])]
used = [0 for _ in range(n)]

num_color = 0
while sum(used) < n:
    for ai, i in enumerate(argsort):
        if used[i] == 0:
            st_ai = ai
            st_i = i
            used[i] = 1
            break
    num_color += 1
    for i in argsort[st_ai+1:]:
        if used[i] == 0 and st_i < i and alist[st_i] != alist[i]:
            st_i = i
            used[i] = 1

print(num_color)