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)

def search(m,l): #startCは常に満たす、stopC+1は常に満たさない
  n=len(l)
  if l[0]<=m: return 0
  elif l[n-1]>m: return n
  startC,stopC=0,n-1
  while stopC-startC!=1:
    #print(l[startC:stopC])
    if l[startC+(1+stopC-startC)>>1]<=m:
      stopC=startC-1+(1+stopC-startC)>>1
    else:
      startC+=(1+stopC-startC)>>1
  return stopC
 
n=int(input())
l=list(map(int,input().split()))
l.sort(reverse=True)
ans=0
for i in range(n-2):
  for j in range(i+1,n-1):
    #print("ans***",ans,l[i]-l[j],l[j+1:])
    ans+=search(l[i]-l[j],l[j+1:]) #l[i]-l[j]<l[ans-1]を満たす最大のans-1を求める
print(ans)