101344: [AtCoder]ABC134 E - Sequence Decomposing

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

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.

Input

题意翻译

给你一个长度为 $N$ 的整数序列:$A=\{A_1,A_2,A_3,\cdots,A_N\}$,对于 $N$ 个整数,我们可以为每一个整数涂上颜色。但要求满足下面这个条件: > 如果 $A_i$ 与 $A_j$ 被涂上同一种颜色,那一定满足 $A_i < A_j$。 找到满足上述条件的最小颜色数。 By [$\texttt{\color{black}Coros-Trusds}$](https://www.luogu.com.cn/user/430409)

加入题单

上一题 下一题 算法标签: