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: Accepted)

import sys
from math import ceil, floor
from collections import deque, Counter, defaultdict
from fractions import gcd
from bisect import bisect_right
input = lambda: sys.stdin.readline().rstrip()


def eprint(s):
    sys.stderr.write('DEBUG: {}'.format(s))
    return


def main():
    n = int(input())
    Ls = list(map(int, input().split()))
    Ls.sort()
    cnt = 0
    for i in range(0,n-2):
        for j in range(i+1,n-1):
            #k以下なら良い
            k =  Ls[i] + Ls[j] -1
            # bisect_right(Ls, k)個の要素が左にある
            # 答え: bisect_right(Ls, k) - j
            cnt += max(bisect_right(Ls, k) - j-1, 0)
            # print(Ls, Ls[i],Ls[j],k, bisect_right(Ls,k)-j-1)
            #012345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576
    print(cnt)
            

if __name__ == '__main__':
    main()