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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>

#define ll long long
#define mp make_pair
#define rep(i, a, b) for(int i = (a); i <= (b); i++)
#define per(i, a, b) for(int i = (a); i >= (b); i--)

using namespace std;

typedef pair<int, int> pii;
typedef double db;
const int N = 1e6 + 50;
int n, a[N], ans = 0, p;
inline int read(){
	int x = 0, f = 1;
	char ch = getchar();
	while(ch < '0' || ch > '9') { if(ch == '-') f = -1; ch = getchar();}
	while(ch >='0' && ch <='9') { x = (x<<3)+(x<<1)+(ch^48); ch = getchar();}
	return x*f;
}
void init(){
	n = read(); 
	rep(i, 1, n) a[i] = read();
	sort(a+1, a+n+1);
	rep(i, 1, n) {
		int l = i+1, r = l+1;
		while(l <= r && l < n) {
			while(a[i] + a[l] > a[r] && r <= n) r++;
			ans += r-l-1; 
			l++;
		} 
	}
	printf("%d\n", ans);
}
int main(){
//	freopen("input.in","r",stdin);
//	freopen("output.out","w",stdout);
	init();
	return 0;
}