Problem:
Score : 400 points

Problem Statement

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

Constraints

Print the number of different triangles that can be formed.

Sample Input 1

4
3 4 2 1

Sample Output 1

1

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

Sample Input 2

3
1 1000 1

Sample Output 2

0

No triangles can be formed.

Sample Input 3

7
218 786 704 233 645 728 389

Sample Output 3

23

Solution in Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

import java.util.*

class D() {
  val sc = Scanner(System.`in`)
  val N: Int = sc.nextInt()
  var L = mutableListOf<Int>()
  var ans: Int = 0
  
  
  init {
      for (i in 1..N) {
    	L.add(sc.nextInt())
      }
  }
  
  fun solve() {
    for (i in 0..N-3) {
      for (j in i+1..N-2) {
        for (k in j+1..N-1) {
          val a: Int = L[i]
          val b: Int = L[j]
          val c: Int = L[k]
          if (a<b+c && b<a+c && c<a+b) {
            ans += 1
          }
        }
      }
    }
    println(ans)
  }

}


fun main(args: Array<String>) {
  D().solve()
}