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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

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


#新しい値が最小なら追加，そうでなければそれを超えない最大の値を書き換え
#降順
b=[]
b.append(A[0])


def bi_s(n):
    if b[-1]>=n:
        return -1
    if n>=b[0]:
        return 0
    
    ceil=0
    floor=len(b)-1
    med=1#len(b)==2のとき
    while abs(floor-ceil)>1:
        med=(ceil+floor)//2
        if n>b[med]:
            floor=med
        else:
            ceil=med
    return floor

for i in range(1,N):
    index=bi_s(A[i])
    if index==-1:
        b.append(A[i])
    else:
        b[index]=A[i]
print(len(b))