Making Triangle

AtCoder

IDabc175_b

Time2000ms

Memory256MB

Difficulty—

We have sticks numbered $1, \cdots, N$. The length of Stick $i$ $(1 \leq i \leq N)$ is $L_i$. In how many ways can we choose three of the sticks with different lengths that can form a triangle? That is, find the number of triples of integers $(i, j, k)$ $(1 \leq i < j < k \leq N)$ that satisfy both of the following conditions: * $L_i$, $L_j$, and $L_k$ are all different. * There exists a triangle whose sides have lengths $L_i$, $L_j$, and $L_k$. ## Constraints * $1 \leq N \leq 100$ * $1 \leq L_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $L_1$ $L_2$ $\cdots$ $L_N$ [samples]

Samples

Input #1

5
4 4 9 7 5

Output #1

5

The following five triples $(i, j, k)$ satisfy the conditions: $(1, 3, 4)$, $(1, 4, 5)$, $(2, 3, 4)$, $(2, 4, 5)$, and $(3, 4, 5)$.

Input #2

6
4 5 4 3 3 5

Output #2

8

We have two sticks for each of the lengths $3$, $4$, and $5$. To satisfy the first condition, we have to choose one from each length.
There is a triangle whose sides have lengths $3$, $4$, and $5$, so we have $2 ^ 3 = 8$ triples $(i, j, k)$ that satisfy the conditions.

Input #3

10
9 4 6 1 9 6 10 6 6 8

Output #3

Input #4

2
1 1

Output #4

0

No triple $(i, j, k)$ satisfies $1 \leq i < j < k \leq N$, so we should print $0$.

API Response (JSON)

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    "name": "Making Triangle",
    "description": {
      "content": "We have sticks numbered $1, \\cdots, N$. The length of Stick $i$ $(1 \\leq i \\leq N)$ is $L_i$. In how many ways can we choose three of the sticks with different lengths that can form a triangle? That i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc175_b"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have sticks numbered $1, \\cdots, N$. The length of Stick $i$ $(1 \\leq i \\leq N)$ is $L_i$.\nIn how many ways can we choose three of the sticks with different lengths that can form a triangle?\nThat i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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