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:
import math

tri = []
fact = []
fact.append(0)
fact.append(1)
tri.append(0)
tri.append(1)
for i in range(2, 1001):
	value = ((i+1)*(i))/2
	tri.append(value)
	cnt = 2
	k = 2
	while k <= math.sqrt(value):
		if value % k == 0:
			cnt += 2
		k+=1
	if int(math.sqrt(value)) * int(math.sqrt(value)) == value:
		cnt -= 1
	fact.append(cnt)
	
#print tri
#print fact
t = input()
while t>0:
	t-=1
	n = input()
	res = 0
	for i in range(1, len(fact)+1):
		if fact[i] > n:
			print tri[i]
			break