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: Wrong Answer)

#coding : utf-8

import os
import sys

class Color:
	def __init__(self, v):
		self.start = v
		self.maxv = v

def get_min(colors):
	return min(colors, key = lambda x: x.start).start

def get_max_index(colors):
	maxv = max(colors, key = lambda x: x.maxv).maxv
	
	for i, c in enumerate(colors):
		if colors[i].maxv == maxv:
			return i

N = int(input())

A = []

for i in range(N):
	A.append(int(input()))

#print(N)
#print(A)

colors = [Color(A[0])]

for i in range(1, N):
	v = A[i]

	minv = get_min(colors)
	
	if v <= minv:
		colors.append(Color(v))

	else:
		idx = get_max_index(colors)
		colors[idx].maxv = v

print(len(colors))