This problem is a programming version of Problem 12 from projecteuler.net
The sequence of triangle numbers is generated by adding the natural numbers. So the 'th triangle number would be . The first ten terms would be:
Let us list the factors of the first seven triangle numbers:
We can see that is the first triangle number to have over five divisors.
What is the value of the first triangle number to have over divisors?
Input Format
First line , the number of testcases. Each testcase consists of in one line.
Constraints
Output Format
For each testcase, print the required answer in one line.
Sample Input
4
1
2
3
4
Sample Output
3
6
6
28
Explanation
Explained in statement.