Contest Duration: - (local time) (100 minutes) Back to Home
D - Distinct Trio /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• 1\leq i \lt j \lt k \leq N
• A_i,A_j,A_k は相異なる

### 制約

• 3 \leq N \leq 2\times 10^5
• 1 \leq A_i \leq 2\times 10^5
• 入力に含まれる値は全て整数である

### 入力

N
A_1 A_2 \ldots A_N


### 入力例 1

4
3 1 4 1


### 出力例 1

2


### 入力例 2

10
99999 99998 99997 99996 99995 99994 99993 99992 99991 99990


### 出力例 2

120


### 入力例 3

15
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9


### 出力例 3

355


Score : 400 points

### Problem Statement

You are given a sequence of length N: A=(A_1,A_2,\ldots,A_N).
Find the number of triples (i,j,k) that satisfy both of the following conditions.

• 1\leq i \lt j \lt k \leq N
• A_i, A_j, and A_k are distinct.

### Constraints

• 3 \leq N \leq 2\times 10^5
• 1 \leq A_i \leq 2\times 10^5
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N


### Sample Input 1

4
3 1 4 1


### Sample Output 1

2


The two triples (i,j,k) satisfying the conditions are (1,2,3) and (1,3,4).

### Sample Input 2

10
99999 99998 99997 99996 99995 99994 99993 99992 99991 99990


### Sample Output 2

120


### Sample Input 3

15
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9


### Sample Output 3

355