Project Euler #42: Coded triangle numbers

_{This problem is a programming version of Problem 42 from projecteuler.net}

The term of a sequence of triangle numbers is given by,

so the first ten triangle numbers are:

You are given an integer. If it is a triangular number , print the term corresponding to this number, else print

Input Format

First line of input contains an integer denoting the number of testcases. Each of the next lines contains an integer.

Constraints

Output Format

Print the answer corresponding to each test case in a new line.

Sample Input

Sample Output

-1
2
10