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)

N = int(input())
A = [0] * N
for i in range(N):
  A[i] = int(input())
  
dp = [-1] * N
count = 0
dp[count] = A[0]
if N ==1:
  print(1)
  exit()

for i in range(1, N):
#  print( 'i_' + str(i))
#  print('A')
#  print(A)
#  print(dp)
  if A[i] <= dp[count]:
    count += 1
    dp[count] = A[i]
  else:
    for j in range(count):
#      print('B')
#      print('count_' + str(count))
#      print('j_' + str(j))
#      print('A[i]_'+ str(A[i]))
#      print('dp[j]_' + str(dp[j]))
      if A[i] <= dp[j] and A[i] > dp[j+1]:
        dp[j+1] = A[i]
        continue
      continue
print(count+1)