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: Accepted)

def main():
    from heapq import heappop, heappush
    import sys

    input = sys.stdin.readline

    N = int(input())
    a = [int(input()) for _ in range(N)]

    def binary_search(b, x):
        ok, ng = len(b), -1
        while abs(ok - ng) > 1:
            mid = (ok + ng) // 2
            if b[mid] < x:
                ok = mid
            else:
                ng = mid
        return ok

    b = [-1]
    for x in a:
        i = binary_search(b, x)
        if i == len(b):
            b.append(x)
        else:
            b[i] = x

    ans = len(b)

    print(ans)


if __name__ == '__main__':
    main()

# import sys
#
# sys.setrecursionlimit(10 ** 7)
#
# input = sys.stdin.readline
# rstrip()
# int(input())
# map(int, input().split())