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 Java (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
import java.util.Arrays;
import java.util.Collections;
 
class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    Integer[] L= new Integer[N];
    for(int i = 0;i<N;i++){
      L[i]=sc.nextInt();
      }
    int r = 0;
    Arrays.sort(L,Collections.reverseOrder());
    for (int i = 0;i<N-2;i++){
      for(int k = i+1;k<N-1;k++){
        int invm = -1;
        int invs = -1;
        int m = L[i]+L[k];
        int s = L[i]-L[k];
        int Mstart = 0;
        int Sstart = 0;
        if(L[k+(N-k)/2]>=m) Mstart = (N-k)/2;
        if(L[k+(N-k)/2]>s) Sstart = (N-k)/2;
        for(int j = 0;j<(N-k)/2;j++){
          if(invm == -1 &&k+Mstart+j+1<N&&L[k+Mstart+j+1]<m){
            invm = k+Mstart+j;
          }
          if(invs ==-1 &&k+Sstart+j+1<N&&L[k+Sstart+j+1]<=s){
            invs = k+Sstart+j;
          }
        }
        if(invs == -1) invs = N-1;
        if(invs>invm) r+=invs-invm;
      }
    }
    System.out.println(r);
  }
}