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)

import bisect
import sys
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))
ans = int(0)

N = I()
color = []
a = I()
maxcolor =[]
maxcolor.append(a)
lena = 1
for i in range(N-1):
    a = I()
    minmaxcolor = min(maxcolor)
    if a<=minmaxcolor:
        maxcolor.insert(0,a)
#        maxcolor.append(a)
        lena += 1
    else:
        acandi = bisect.bisect_left(maxcolor, a)
        maxcolor[acandi-1] = a
        """
        aupper = lena-1
        alower = int(0)
        acandi = aupper//2
        
        for _ in range(aupper+1):
            if maxcolor[acandi]>=a:
                alower = acandi
                acandi = (aupper+acandi+1)//2
            else:
                if aupper - alower <= 1:
                    maxcolor[acandi] = a
                    break
                else:
                    aupper = acandi
                    acandi = (acandi + alower) // 2
        """

#print(maxcolor)
ans = len(maxcolor)
print(ans)