Triangles

AtCoder

IDabc143_d

Time2000ms

Memory256MB

Difficulty—

Takahashi has $N$ sticks that are distinguishable from each other. The length of the $i$\-th stick is $L_i$. He is going to form a triangle using three of these sticks. Let $a$, $b$, and $c$ be the lengths of the three sticks used. Here, all of the following conditions must be satisfied: * $a < b + c$ * $b < c + a$ * $c < a + b$ How many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them. ## Constraints * All values in input are integers. * $3 \leq N \leq 2 \times 10^3$ * $1 \leq L_i \leq 10^3$ ## Input Input is given from Standard Input in the following format: $N$ $L_1$ $L_2$ $...$ $L_N$ [samples]

Samples

Input #1

4
3 4 2 1

Output #1

1

Only one triangle can be formed: the triangle formed by the first, second, and third sticks.

Input #2

3
1 1000 1

Output #2

0

No triangles can be formed.

Input #3

7
218 786 704 233 645 728 389

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Triangles",
    "description": {
      "content": "Takahashi has $N$ sticks that are distinguishable from each other. The length of the $i$\\-th stick is $L_i$. He is going to form a triangle using three of these sticks. Let $a$, $b$, and $c$ be the le",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc143_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi has $N$ sticks that are distinguishable from each other. The length of the $i$\\-th stick is $L_i$.\nHe is going to form a triangle using three of these sticks. Let $a$, $b$, and $c$ be the le...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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