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: Runtime Error)

from itertools import groupby 
N = int(input())
As = [int(input()) for _ in range(N)]

def chop(As):
    res = []
    minibatch=[As[0]]
    for i in range(len(As)-1):
        if As[i]<As[i+1]:
            minibatch.append(As[i+1])
        else:
            res.append(minibatch)
            minibatch=[As[i+1]]
    if minibatch:
        res.append(minibatch)
    return res
    
chopped = chop(As)
remains = chopped

def kakutei(remains):
    deletes = []
    for i in range (1,len(remains)):
        if remains[0][-1]<remains[i][0]:
            remains[0].extend(remains[i])
            deletes.append(i)
    x = remains[0].copy()
    for d in deletes[::-1]:
        del remains[d]
    del remains[0]
    return (x,remains)
res = []
while remains:
    x, remains = kakutei(remains)
    res.append(x)
print(len(res))

#N 個の整数からなる数列 A={A1,A2,⋯,AN} が与えられます。 N 個それぞれの整数に対して、色を 1つ選んでその色を塗ります。 この時、以下の条件を満たす必要があります:
#Aiと Aj(i<j) が同じ色で塗られているならば Ai<Aj
#が成立する
#条件を満たすように色を塗る時、用いる色の数の最小値を求めてください。