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)

import bisect
from collections import deque

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

LIS = deque([a[0]])
for i in range(1,N):
    if a[i] > LIS[-1]:
    	LIS[-1] = a[i]
    elif LIS[0] >= a[i]:
    	LIS.appendleft(a[i])
    else:
    	LIS[bisect.bisect_left(LIS, a[i])-1] = a[i]

print(len(LIS))