Let us denote by $d(n)$ the sum of all divisors of the number $n$, i.e. $d(n) = \sum\limits_{k | n} k$.

For example, $d(1) = 1$, $d(4) = 1+2+4=7$, $d(6) = 1+2+3+6=12$.

For a given number $c$, find the minimum $n$ such that $d(n) = c$.

Input

The first line contains one integer $t$ ($1 \le t \le 10^4$). Then $t$ test cases follow.

Each test case is characterized by one integer $c$ ($1 \le c \le 10^7$).

Output

For each test case, output:

• "-1" if there is no such $n$ that $d(n) = c$;
• $n$, otherwise.

见题面 Input 部分

见题面 Output 部分