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: Wrong Answer)

from collections import Counter, defaultdict
import sys
sys.setrecursionlimit(10 ** 5 + 10)
# input = sys.stdin.readline
from math import factorial
import heapq, bisect
import math
import itertools

import queue
from collections import deque



def main():
    num = int(input())
    data = list(map(int, input().split()))

    data.sort()
    dp = [0 for i in range(max(data) * 2 + 1)]
    count = Counter(data)

    for i in range(1, max(data) * 2 + 1):
        dp[i] = dp[i - 1] + count[i]

    count = sorted(count.items(), key=lambda x: x[0])
    ans = 0

    # print(data)
    # print(count)
    # print(dp)

    for i in range(len(count) - 1):
        if count[i][1] >= 3:
            ans += (count[i][1] * (count[i][1] - 1) * (count[i][1] - 2)) // 6
        if count[i][1] >= 2:
            nokori = count[i][0] * 2 - 1
            ans += (count[i][1] * (count[i][1] - 1)) // 2 * (dp[nokori] - dp[count[i][0]])

        for j in range(i + 1, len(count)):
            max_data = count[i][0] + count[j][0] - 1
            kari = count[i][1] * count[j][1] * (dp[max_data] - dp[count[j][0]])
            ans += kari

    print(ans)








if __name__ == '__main__':
    main()