Odd One Subsequence

AtCoder

IDabc429_c

Time2000ms

Memory256MB

Difficulty—

You are given an integer sequence of length $N$, $A=(A_1,A_2,\ldots,A_N)$. Find the number of triples of integers $(i,j,k)$ satisfying $1\leq i<j<k\leq N$ that satisfy the following condition: > Exactly two distinct values are contained in $A_i,A_j,A_k$. That is, two of $A_i,A_j,A_k$ are equal, and the remaining one is different. ## Constraints * $3 \leq N \leq 2\times 10^5$ * $1 \leq A_i \leq N$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

5
3 2 5 2 2

Output #1

6

For example, $(i,j,k)=(1,2,4)$ satisfies the condition because exactly two distinct values, $2$ and $3$, are contained in $A_1=3$, $A_2=2$, and $A_4=2$.  
Including this, the six triples $(i,j,k)=(1,2,4),(1,2,5),(1,4,5),(2,3,4),(2,3,5),(3,4,5)$ satisfy the condition.  
Therefore, print $6$.

Input #2

3
1 1 1

Output #2

0

There may be no triples that satisfy the condition.

API Response (JSON)

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