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 Lua (5.3.2) (judge verdict: Accepted)

local function upper_bound(key,ary)
    local n=#ary
    if n==0 then
        return 1 
    end
    if key<ary[1] then
        return 1
    end
    if key>=ary[n] then
        return n+1
    end
    local min,max=1,n
    while 1<max-min do
        local mid=(min+max)//2
        if key>=ary[mid] then
            min=mid
        else
            max=mid
        end
    end
    return max
end

n=io.read("*n","*l")
l={}
for i=1,n do
    l[i]=io.read("*n")
end
table.sort(l)
counter=0
for i=n,3,-1 do
    large=l[i]
    for j=i-1,2,-1 do
        middle=l[j]
        if middle*2<=large then
            break
        end
        local smallmin=upper_bound(large-middle,l)
        if smallmin<j then
            counter=counter+j-smallmin
        end
    end
end
print(counter)