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>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <float.h>
 
#pragma region 定義
#define i_cin(X) scanf("%d", &X)
#define i_cin2(X,Y) scanf("%d %d",&X,&Y)
#define i_cin4(X,Y,Z,W) scanf("%d %d %d %d",&X,&Y,&Z,&W)
#define i_cin3(X,Y,Z) scanf("%d %d %d",&X,&Y,&Z)
#define l_cin(X) scanf("%ld",&X)
#define f_cin(X) scanf("%f",&X)
#define l_cin2(X,Y) scanf("%ld %ld",&X,&Y)
#define s_cin(X) scanf("%s",&X)
#define ll_cin(X) scanf("%lld", &X)
 
#define  i_cout(X) printf("%d\n",X)
#define  f_cout(X) printf("%g\n",X)
#define  i_cout2(X,Y) printf("%d %d\n",X,Y)
#define  l_cout(X) printf("%ld\n",X)
#define  s_cout(X) printf("%s\n",X)
#define  ll_cout(X) printf("%lld\n",X)
 
typedef long long  ll;
#define rept(x, s, n) for (int x = s; x < n; x++)
 
#define S_RTN(S)  s_cout(S);return 0
 
 
#define _itoa(A,N) sprintf(A, "%d", N);
 
int i_cins(int n, int* A);
int l_cins2(int n, long* A, long* B);
int s_dsort(const void* a, const void* b);
int s_asort(const void* a, const void* b);
 
int  _gcd(int a, int b);
int  _swp(int* a, int* b);
int _cknum(char* a, int n);
int _atoi(char* s, int len);
 
 
int s_asorts(const void* a, const void* b);
 
//昇順
int s_asorts(const void* a, const void* b) {
    return(strcmp((char*)a, (char*)b));
}
int s_dsort(const void* a, const void* b) {
    return(*(int*)b - *(int*)a);
}
int s_asort(const void* a, const void* b) {
    return(*(int*)a - *(int*)b);
}
int l_cins2(int n, long* a, long* b) {
    int i;
    rept(i, 0, n) {
        l_cin2(*(a + i), *(b + i));
    }
    return 0;
}
int i_cins(int n, int* a) {
    int i;
    for (i = 0; i < n; i++) {
        i_cin(*(a + i));
    }
 
    return 0;
}
int _gcd(int a, int b) {
    int r, tmp;
    if (a < b) { tmp = a; a = b; b = tmp; }
    r = a % b;
    while (r) {
        if (!r) break;
        a = b; b = r;
        r = a % b;
    }
    return(b);
}
 
long _max(long a, long b) {
    return a > b ? a : b;
}
long _min(long a, long b) {
    return a < b ? a : b;
}
int _swp(int* a, int* b)
{
    int tmp;
    tmp = *b; *b = *a; *a = tmp;
    return 0;
}

//大きい順
int compare_int(const void *a, const void *b)
{
    return *(int*)b - *(int*)a;
}

//変換(文字から整数)
int ctoi(char c) {
    if (c >= '0' && c <= '9') {
        return c - '0';
    }
    return 0;
}


int main(void){
    int N;
    int cnt=0;
    i_cin(N);
    int len[N];
    rept(i,0,N)
    i_cin(len[i]);
    for(int i=0;i<N-2;i++){
        for(int j=i+1;j<N-1;j++){
            for(int k=j+1;k<N;k++){
                if(len[k]<(len[i]+len[j]) && len[i]<(len[j]+len[k]) && len[j]<(len[k]+len[i]))
                    cnt++;
            }
        }
    }
    printf("%d",cnt);
}