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)

a=int(input())
b=[int(input()) for i in range(a)]
LIS = [b[0]]
for i in range(1,len(b)):
  if b[i] <= LIS[-1]:
    LIS.append(b[i])
  else:
    lo=0
    hi=len(LIS)
    while lo < hi:
      mid=(lo+hi)//2
      if b[i]>LIS[mid]:
        hi =mid
      else:
        lo=mid+1  
    LIS[lo] = b[i]
print(len(LIS))