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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var i,j,k,l,o,p,count,n,cautpetrea:longint;
type vector = array[1..2010] of longint;
var x:vector;
function check(a,b:longint):boolean;
begin
if a<b then check:=true
else check:=false;
end;
function cautbin(stanga,dreapta,valoari:longint):longint;
var mid,rs:longint;
begin
rs:=stanga-1;
while stanga<=dreapta do begin
  mid:=(stanga+dreapta) div 2;
  if check(x[mid],valoari) then begin
    rs:=mid;
    stanga:=mid+1;
    end
  else dreapta:=mid-1;
  end;
cautbin:=rs;
end;
  

function triunghi(a,b,c:longint):boolean;
begin
if (a+b>c) and (a+c>b) and (c+b>a) then begin
  // writeln(a,' ',b,' ',c);
   triunghi:=true;
   end
else  begin
  //writeln(a,' ',b,' ',c);
  triunghi:=false;
  end;
end;
procedure swap(var a,b:integer);
var temp:integer;
begin
temp:=a;
a:=b;
b:=temp;
end;
procedure bubleSort(var a:vector;n:longint);
var i,j:longint;
isSwapped:boolean;
begin
for i:=1 to n do begin
            isSwapped:=false;
                for j:=1 to n-i do 
                            if a[j]> a[j+1] then begin
                                              swap(a[j],a[j+1]);
                                              isSwapped:=true;
                                              end;
                if not isSwapped then break;
                end;
                        

end;
begin
read(n);
for i:=1 to n do 
  read(x[i]);
bublesort(x,n);
for i:=1 to n do
  for j:=i+1 to n do begin
    cautpetrea:=+cautbin(j,n,x[i]+x[j]);
    if cautpetrea>j then count:=count+(cautpetrea-j);
    end;
writeln(count);
end.