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 sys
from bisect import bisect_right, insort_left
from heapq import *
N = int(sys.stdin.readline())
a_list = [int(sys.stdin.readline()) for _ in range(N)]


que = []
heapify(que)
ans = 0
min_num = float("inf")
for i, a in enumerate(a_list):
    if i == 0:
        que.append(a)
        min_num = a
        ans += 1
    else:
        # idx = bisect_right(que, a-1)
        if a <= min_num:
        # if idx == 0:
            heappush(que, a)
            ans += 1
            min_num = a
        else:
            idx = bisect_right(que, a-1)
            que[idx-1] = a
            if idx -1 == 0:
                min_num = a
    #print(que, min_num)
print(ans)