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())
AN=[int(input()) for _ in range(N)]

ite=0
ret=1
tmp=0
leng=N
flg=False
#print()
while leng > 0:
    #print(tmp,ite,AN[ite],ret)
    if (flg==False)and ite==0:
        flg=True
        tmp=AN.pop(ite)
        leng-=1
        continue
    if tmp < AN[ite]:
        tmp=AN.pop(ite)
        leng-=1
    else:
        ite+=1
        if ite >= leng:
            ite=0
            tmp=0
            flg=False
            ret+=1

print(ret)