IITWPC4B  Maggu and Triangles
Maggu has a wire of length n. He has to make triangles out of it such that the side lengths of each triangle are integers. He now wants to know the number of distinct (not congruent) triangles that he can create using the wire of length n. Note that he has to use all of the wire in making the triangle.
Input
First line contains T: number of test cases. (1 <= T <= 10^5)
For each test case, there is a single line containging an integer n (n >= 1 && n <= 10^9)
Output
Each test case output a single integer representing the number of triangles he can create.
Example
Input:
3
5
7
9 Output:
1
2
3
hide comments
Liquid_Science:
20160123 13:17:41
faltu question _ 

kp101110000:
20160117 17:07:26
waste of time


Shashank Tiwari:
20151223 23:18:23
Don't waste your time on this question. This is based on mathematical formula. Just google. You will only benefit if you delve into deriving it else waste of time. Make sure that formula has rounding function and not ceiling or floor. Last edit: 20151223 23:19:05 

Siddharth Singh:
20151210 14:49:22
Shantanu's Comment Really Helped :) 

shantanu tripathi:
20150831 21:33:13
http://mathworld.wolfram.com/AlcuinsSequence.html


sushilverma:
20150324 18:40:17
why is it 3 for n=9 

AlcatraZ:
20140305 23:45:48
for n=5, the only valid triangle which can be formed is of sides 1,2,2. hence ans is 1. ;)


$iddharth prasad:
20140206 08:59:53
@Ankush Jain ans for n=4 is 0 

Ankush Jain:
20140205 23:52:22
What is the answer for n = 4? In general, do we have to consider cases where area of formed triangle is 0? (I used a popular theorem available online, and it did not get accepted). 
Added by:  praveen123 
Date:  20140131 
Time limit:  2s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  IITK ACA CSE online judge 