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 (7.3.0) (judge verdict: Accepted)

def is_ok1(a,b,c):
    return L[b] < L[c] + L[a]
def is_ok2(a,b,c):
    return L[c] < L[a] + L[b]
def meguru_bisect(ng, ok, is_ok, a, b):
    '''
    初期値のng,okを受け取り,is_okを満たす最小(最大)のokを返す
    まずis_okを定義すべし
    ng ok は  とり得る最小の値-1 とり得る最大の値+1
    最大最小が逆の場合はよしなにひっくり返す
    '''
    while (abs(ok - ng) > 1):
        mid = (ok + ng) // 2
        if is_ok(a, b, mid):
            ok = mid
        else:
            ng = mid
    return ok
N = int(input())
L = sorted(list(map(int, input().split())))
ans = 0
for a in range(N):
    for b in range(a+1, N):
        ans += max(0, meguru_bisect(N, b, is_ok2, a, b)-meguru_bisect(b, N, is_ok1, a, b)+1)
print(ans)