Contest Duration: - (local time) (100 minutes) Back to Home
C - Snuke Festival /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

りんごさんが作ることのできる祭壇は何種類あるでしょうか。ただし、2 つの祭壇が異なるとは、上部、中部、下部に使われるピースのうち 少なくとも 1 つが異なることを言います。

### 制約

• 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)
• 入力は全て整数である

### 入力

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


### 出力

りんごさんが作ることのできる祭壇の種類数を出力せよ。

### 入力例 1

2
1 5
2 4
3 6


### 出力例 1

3


• 上部に 1 個目、中部に 1 個目、下部に 1 個目のパーツを使った祭壇
• 上部に 1 個目、中部に 1 個目、下部に 2 個目のパーツを使った祭壇
• 上部に 1 個目、中部に 2 個目、下部に 2 個目のパーツを使った祭壇

### 入力例 2

3
1 1 1
2 2 2
3 3 3


### 出力例 2

27


### 入力例 3

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


### 出力例 3

87


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