NOTATRI  Not a Triangle
You have N (3 ≤ N ≤ 2,000) wooden sticks, which are labeled from 1 to N. The ith stick has a length of L_{i} (1 ≤ L_{i} ≤ 1,000,000). Your friend has challenged you to a simple game: you will pick three sticks at random, and if your friend can form a triangle with them (degenerate triangles included), he wins; otherwise, you win. You are not sure if your friend is trying to trick you, so you would like to determine your chances of winning by computing the number of ways you could choose three sticks (regardless of order) such that it is impossible to form a triangle with them.
Input
The input file consists of multiple test cases. Each test case starts with the single integer N, followed by a line with the integers L_{1}, ..., L_{N}. The input is terminated with N = 0, which should not be processed.
Output
For each test case, output a single line containing the number of triples.
Example
Input: 3 4 2 10 3 1 2 3 4 5 2 9 6 0 Output: 1 0 2
For the first test case, 4 + 2 < 10, so you will win with the one available triple. For the second case, 1 + 2 is equal to 3; since degenerate triangles are allowed, the answer is 0.
hide comments
ntnguyen:
20200129 07:06:11
Note: Do "not" print a new line after the output ends.


subodh898:
20191108 15:27:48
upper_bound search 

jvjplus:
20190922 04:01:51
Simple calculation. The sum of the two sides < the third side 

sanket17:
20190806 11:12:18
my n*n*log(n) got tle


sanjay_thiru:
20190629 11:29:08
Nice question! 

nishit5:
20190625 16:30:52
pls be aware of the input format it cost me one WA 

abhimanyu_1998:
20190325 18:15:33
AC in 1 go


y17prashant:
20190322 03:15:55
SImple implementation can be done no need of bin search 

ankur1999:
20190202 14:48:32
Use upper_bound(Time: 0.14s) instead of binary search(Time: 0.18s),


sajalagrawal14:
20190129 15:26:11
AC in one go!!!!!! n2logn complexicity 
Added by:  Neal Wu 
Date:  20080803 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO 