United Cows of Farmer John

문제

The United Cows of Farmer John (UCFJ) are sending a delegation to the International bOvine olympIad (IOI).

There are $NN$ cows participating in delegation selection ($1\le N\le 2\cdot {10}^{5}1\; \backslash leq\; N\; \backslash leq\; 2\; \backslash cdot\; 10^5$). They are standing in a line, and cow $ii$ has breed $b_{i}b\_i$.

The delegation will consist of a contiguous interval of at least three cows - that is, cows $l\dots rl\backslash ldots\; r$ for integers $ll$ and $rr$ satisfying and $r-l\ge 2r-l\backslash ge\; 2$. Three of the cows in the chosen interval are marked as delegation leaders. For legal reasons, the two outermost cows of the chosen interval must be leaders. Moreover, to avoid intra-breed conflict, every leader must be of a different breed from the rest of the delegation (leaders or not).

Help the UCFJ determine (for tax reasons) the number of ways they might choose a delegation to send to the IOI. Two delegations are considered different if they have different members or different leaders.

입력

The first line contains $NN$.

The second line contains $NN$ integers $b_1,b_2,\dots ,b_{N}b\_1,b\_2,\backslash ldots,b\_N$, each in the range $[1,N][1,N]$.

출력

The number of possible delegations, on a single line.

Note that the large size of integers involved in this problem may require the use of 64-bit integer data types (e.g., a "long long" in C/C++).

힌트

Each delegation corresponds to one of the following triples of leaders:

$$(1,2,3),(1,2,4),(1,3,4),(1,4,7),(2,3,4),(4,5,6),(4,5,7),(4,6,7),(5,6,7)\mathrm{.}(1,2,3),(1,2,4),(1,3,4),(1,4,7),(2,3,4),(4,5,6),(4,5,7),(4,6,7),(5,6,7).$$

7
1 2 3 4 3 2 5

9