import Control.Applicative
import Control.Monad
import System.IO
import Prelude
import Data.List

isqrt :: Int -> Int -- Thanks StackOverflow
isqrt = ceiling . sqrt . fromIntegral

triangle_num :: Int -> Int
triangle_num n = (n * (n + 1)) `div` 2

triangle_nums = map triangle_num [1..]

primes = 2 : [i | i <- [3..1000],  
              and [rem i p > 0 | p <- takeWhile (\p -> p^2 <= i) primes]]

num_subdivisions :: Int -> Int -> Int -> Int
num_subdivisions num divisor rem
    | num `mod` divisor /= 0 = rem
    | otherwise = num_subdivisions (num `div` divisor)  divisor (rem+1)

num_divisors :: Int -> Int
num_divisors 1 = 1
num_divisors n = product [((num_subdivisions n x 0) + 1) | x <- (filter (<= ((isqrt n) + 1)) primes), n `mod` x == 0]

smallestTri :: Int -> [Int] -> Int
smallestTri n xs
    | num_divisors (head xs) > n = head xs
    | otherwise = smallestTri n (tail xs)

main :: IO ()
main = do
    t_temp <- getLine
    let t = read t_temp :: Int
    forM_ [1..t] $ \a0  -> do
        n_temp <- getLine
        let n = read n_temp :: Int
        let smallTri = smallestTri n triangle_nums
        print(smallTri)