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)

N = int(input())
a = []
for i in range(N):
        x = int(input())
        a.append(x)
c = [0 for i in range(N)]
color = 0
for i in range(N-1,-1,-1):
        if c[i]: continue
        color += 1
        #print(color)
        x = a[i]
        c[i] = 1
        for j in range(i-1,-1,-1):
                if c[j]: continue
                if x > a[j]:
                        x = a[j]
                        c[j] = 1
                        #print("x:{}".format(x))
                #print("i:{}, j:{}, c:{}".format(i,j,c))
print(color)