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)

import bisect
def LIS():
    L[0] = A[0]
    length = 1
    for i in range(1, N):
        print(A[i])
        if L[length-1] < A[i]:
            L[length] = A[i]
            length += 1
        else:
            j = bisect.bisect_left(L, A[i])
            L[min(length-1, j)] = A[i]
    return length

def LISDesc():
    L[0] = A[-1]
    length = 1
    for i in range(N-2, -1, -1):
        if L[length-1] <= A[i]:
            L[length] = A[i]
            length += 1
        else:
            j = bisect.bisect_left(L, A[i])
            print(i, A[i], j)
            L[min(length-1, j)] = A[i]
    return length

INFTY = 10**13
N = int(input())
A = [int(input()) for i in range(N)]
L = [INFTY for i in range(N)]
ans = LISDesc()
print(ans)
print(L)