TRICOUNT - Counting Triangles


We define the LEVEL of a triangle as in the following illustrative image:

Task: Your task is very easy. All you have to do is to count all triangles in the biggest one (Level N).

Input

The first line of the input contains an integer T (T ≤ 10000) - the number of test cases and T lines follow. Each line contains an integer N (1 ≤ N ≤ 106) which is the level of the triangle in that test case.

Output

For each test case, you should write a seperate line: the number of triangles in the biggest one (Level N). (All answers will fit within the range of a 64-bit integer)

Example

Input:
3
1
2
3

Output:
1
5
13

Source limit is 500 bytes.


hide comments
theabd123: 2018-05-29 15:14:03

note there is different formula for even and odd values of N

akshat7321: 2018-05-25 13:45:02

Method apart from formula: observe the pattern of the number of triangles facing upward and downward. Store upward and downward triangles in 2 arrays and add them to get the answer.

archit4077sh: 2018-05-23 22:25:16

Hey i just derived a recurrence for this
f(n) = 3* (f(n-1)-f(n-2)) + f(n-3) + 2 if n is even
f(n) = 3* (f(n-1)-f(n-2)) + f(n-3) + 1 if n is odd
with base cases f(1)=1 , f(2)=5 ,f(3)=13
Hint: Use principle of inclusion and exclusion...

Last edit: 2018-05-23 22:28:19
summer_2: 2018-05-23 19:14:11

explain the solution please?
I want to know how that formula comes?

Last edit: 2018-05-23 19:15:31
shubham31: 2018-05-11 12:08:29

(n^2) + [ (n(n-1)/2] * [(3+(2*n - 1))/6], shows wrong answer... cross checked it. still no success.

n(n+2)(2n+1)/8 works but obviously on calculation for n=3 gives a wrong value. (bad test cases)

riyadhrazzaq: 2018-03-24 18:25:35

There's two version of the formula. One uses floor function , another uses odd-even condition. I've used both of them and only got AC for odd-even condition. Can anybody explain that ?

kkislay20: 2018-03-10 08:58:48

Use the direct formula...and long long int and you are good to go.

bradyawn: 2018-01-24 00:15:38

For those who are wondering why n = 3 is not 9, it is because triangle of not size 1 also count

srjsunny: 2018-01-23 14:37:20

use P and C you will get triangles=n(n+2)(2n+1)/8

vikramvarun: 2018-01-12 11:07:58

SPOJ is the worst platform to practice coding. Gives TLE in R for simple operations as well. Do the admins/moderators do any work at all? Can't they see that time limit should be adjusted according to language.


Added by:nha.duong
Date:2007-08-05
Time limit:1s
Source limit:500B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 ERL JS-RHINO NODEJS OBJC PERL6 SQLITE VB.NET
Resource:Trần Huy Hưng