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: Accepted)

n = int(input())
a = []
for _ in range(n):
    a.append(int(input()))

stack = []

def bisect(li, i):
    if len(li)==0:
        li.append(i)
        return
    ok = len(li)
    ng = -1
    while abs(ok-ng)>1:
        tmp = (ok+ng)//2
        if li[tmp]<i:
            ok = tmp
        else:
            ng = tmp
    if ok < len(li):
        li[ok] = i
    else:
        li.append(i)

for i in a:
    bisect(stack, i)
print(len(stack))