Just Do It

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

Description

Now we define a function F(x), which means the factors of x. In particular, F(1) = 1,since 1 only has 1 factor 1, F(9) = 3, since 9 has 3 factors 1, 3, 9. Now give you an integer k, please find out the minimum number x that makes F(x) = k.

Input

The first line contains an integer t means the number of test cases.
The follows t lines, each line contains an integer k. (0 < k <= 100).

Output

For each case, output the minimum number x in one line. If x is larger than 1000, just output -1.

Sample Input

4
4
2
5
92

Sample Output

6
2
16
-1

lcy

Source

HDU 2009-11 Programming Contest