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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

#!/usr/bin/env python3
import collections
import itertools as it
import math
#import numpy as np
 
#  = input()
n  = int(input())
#  = map(int, input().split())
l  = list(map(int, input().split()))
#  = [int(input()) for i in range(N)]
#
# c = collections.Counter()

l = sorted(l)
#print(l)

ans = 0
for i1 in range(len(l)-2):
    a = l[i1]
    if a >= l[i1+1] + l[i1+2]:
        continue

    for i2 in range(i1+1, len(l)-1):
        b = l[i2]
        if b >= a + l[i2+1]:
            continue

        for i3 in range(i2+1, len(l)):
            if l[i3] < a + b:
                #print(a, b, l[i3])
                ans += 1
            else:
                break

        #l_ = [l[i3] for i3 in range(i2+1, len(l[i2+1:]))]

print(ans)