Problem: Archith loves to play with number series. Archith asked his girlfriend to a date. But she was busy in solving the homework on triangular series which stated that find the least number which has higher divisors than n in a triangular series. His girlfriend made a condition that if he solves this assignment for her she will come for date. Archith dont want to waste time he is developing a code. Put yourself in the position of archith and solve this problem.(#projecteuler 13)

INPUT:
T test cases
every t lines consists of a number n which specifies the no of divisors.
OUTPUT:
output the least triangular number which has higher no of divisors than n.

1<T<11
1<n<10^2

example:

triangular series will be as follows 1,3,6,10........
if n =2
6 has 4 divisors.So 6 will be the least number to have more than n divisors.

SAMPLE INPUT
4
1
2
3
4

SAMPLE OUTPUT
3
6
6
28

Solution (in PYTHON):

Solution:
from math import sqrt
def factors(n):
	final = set()
	for i in xrange(1,int(sqrt(n))+1):
		if n%i == 0:
			final.add(i)
			final.add(n/i)
	return len(final)

for i in range(input()):
	num = input()
	diff = 3
	start = 3
	ans = start
	while factors(start) <= num:
		start += diff
		diff += 1
		ans = start
	print ans