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 C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<stdio.h>
int nibutan(int* a,int i, int j){
    int high=j-1;
    int low=0;
    int mid=0;
    mid=(j-1)/2;
    while(low<=high){
        if(a[mid]>(a[i]-a[j]))high=mid;
        else low=mid+1;
        mid=(high+low)/2;
        if(high==low)break;
    }
    return mid;
}
 


int solve(int* a,int n){
    int res=0;
    for(int i=n-1;i>1;i--){
        for(int j=i-1;j>0;j--){
            int k=nibutan(a,i,j);
            if(a[k]>a[i]-a[j])res+=j-k;
        }
    }
    return res;
}

void swap(int *a,int *b){
    int c;
    c=*a;
    *a=*b;
    *b=c;
}

void sort(int*a, int n){
    for(int i=0;i<n;i++){
        for(int j=i;j<n;j++){
            if(a[i]>a[j])swap(&a[i],&a[j]);
        }
    }
}

int main(void){
    int n;
    scanf("%d",&n);
    int a[n];
    for(int i=0;i<n;i++){
        scanf("%d",&a[i]);
    }
    for(int i=0;i<n;i++){
        sort(a,n);
    }
    printf("%d\n",solve(a,n));
    return 0;
}