200840: [AtCoder]ARC084 C - Snuke Festival

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

Description

Score : $300$ points

Problem Statement

The season for Snuke Festival has come again this year. First of all, Ringo will perform a ritual to summon Snuke. For the ritual, he needs an altar, which consists of three parts, one in each of the three categories: upper, middle and lower.

He has $N$ parts for each of the three categories. The size of the $i$-th upper part is $A_i$, the size of the $i$-th middle part is $B_i$, and the size of the $i$-th lower part is $C_i$.

To build an altar, the size of the middle part must be strictly greater than that of the upper part, and the size of the lower part must be strictly greater than that of the middle part. On the other hand, any three parts that satisfy these conditions can be combined to form an altar.

How many different altars can Ringo build? Here, two altars are considered different when at least one of the three parts used is different.

Constraints

  • $1 \leq N \leq 10^5$
  • $1 \leq A_i \leq 10^9(1\leq i\leq N)$
  • $1 \leq B_i \leq 10^9(1\leq i\leq N)$
  • $1 \leq C_i \leq 10^9(1\leq i\leq N)$
  • All input values are integers.

Input

Input is given from Standard Input in the following format:

$N$
$A_1$ $...$ $A_N$
$B_1$ $...$ $B_N$
$C_1$ $...$ $C_N$

Output

Print the number of different altars that Ringo can build.


Sample Input 1

2
1 5
2 4
3 6

Sample Output 1

3

The following three altars can be built:

  • Upper: $1$-st part, Middle: $1$-st part, Lower: $1$-st part
  • Upper: $1$-st part, Middle: $1$-st part, Lower: $2$-nd part
  • Upper: $1$-st part, Middle: $2$-nd part, Lower: $2$-nd part

Sample Input 2

3
1 1 1
2 2 2
3 3 3

Sample Output 2

27

Sample Input 3

6
3 14 159 2 6 53
58 9 79 323 84 6
2643 383 2 79 50 288

Sample Output 3

87

Input

题意翻译

## 题面: 今年也到了滑雪节的季节。仪式上必须有祭坛,祭坛由上部、中部、下部3个类别的部件各1个构成。 祭坛的3分类的零件各有N个。i上部零件的大小Ai,第i个中部零件的大小Bi,第i个下部的零件的大小是Ci。 在制作祭坛的时候,中部的零件的尺寸要比上部的零件的尺寸大,下部的零件的尺寸必须比中部的零件的尺寸大。反过来说,满足此条件的任意三块组合就可建造祭坛。 问:能做的祭坛有几种?(当上部、中部、下部使用的块中至少有一个是不同的时候,两个祭坛视为不同。) ## 样例1说明: 可以建造以下三种祭坛: 上部使用第1个,中部第1个,下部第1个零件的祭坛 上部使用第1个,中部第1个,下部第2个零件的祭坛 上部使用第1个,中部第2个,下部第2个零件的祭坛

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