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)

def se(c, x, h, l):
    if h == l:
        return l
    t = (h+l)//2
    if c[t] < x:
        a = se(c,x,h,t+1)
    elif c[t] == x:
        return t+1
    else:
        a = se(c,x,t,l)
    return a
        
    
import numpy as np
n = int(input())
a = [int(input()) for i in range(n)]
c = [a[-1]]
if len(np.unique(a)) == 1:
    print(len(a))
else:
    for i in a[::-1][1:]:
        if max(c) <= i:
            c.append(i)
        else:
            c[se(c,i,len(c),0)] = i
    print(len(c))