Positive integers that are convenient for forming various measurement systems are called practical. A positive integer $$$x$$$ will be practical if any natural number less than $$$x$$$ can be represented as the sum of any different divisors of $$$x$$$.

For example, the number $$$6$$$ is practical since using the sum of its divisors $$$1, 2, 3, 6$$$, you can represent any number from $$$1$$$ to $$$6$$$: $$$1 = 1$$$, $$$2 = 2$$$, $$$3 = 3$$$, $$$4 = 1 + 3$$$, $$$5 = 2 + 3$$$, and $$$6 = 6$$$.

On the other hand, the number $$$9$$$ is not practical since, using its divisors $$$1, 3, 9$$$, it is impossible to represent the numbers $$$2, 5, 6, 7$$$ and $$$8$$$.

There are infinitely many practical numbers, and they have many useful properties. In particular:

• the product of two practical numbers is also always a practical number;
• if $$$p$$$ is a practical number, and $$$d$$$ is some kind of its divisor, then their product $$$p \cdot d$$$ is also a practical number;
• one is the only odd number among practical number.

Among the practical numbers, primitive practical numbers stand out - those that cannot be obtained from other practical numbers by multiplying them or multiplying a practical number by any of its divisors.

Write a program that, by the number $$$n$$$, returns the $$$n$$$-th largest primitive practical number.