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 (3.8.2) (judge verdict: Accepted)

import sys
input = sys.stdin.readline
from bisect import bisect_left, bisect_right


def read():
    N = int(input().strip())
    A = [int(input().strip()) for _ in range(N)]
    return N, A


def solve(N, A, INF=10**9+1):
    # LIS
    # dp[i]: 長さiの最長増加部分列(A[i]<A[j])のうち、最も小さい数字
    dp = [INF for i in range(N)]
    for i in range(N):
        a = A[N-i-1]
        idx = bisect_right(dp, a)
        dp[idx] = a
    return bisect_right(dp, INF-1)


if __name__ == '__main__':
    inputs = read()
    outputs = solve(*inputs)
    if outputs is not None:
        print("%s" % str(outputs))