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)

def bs(A, t):
  l, r = 0, len(A) - 1

  while l < r:
    mid = (l + r) // 2
    if t <= A[mid]:
      r = mid - 1
    else:
      l = mid + 1
  else:
    return l


N = int(input().strip())
A = [0] * N

# reverse
for i in range(N):
  A[- i - 1] = int(input().strip())

B = [A[0]]
for i in range(1, N):
  a = A[i]

  if a < B[0]:
    B[0] = a
  elif a >= B[-1]:
    B.append(a)
  else:
    l = bs(B, a)
    B[l] = a

print(len(B))