C. Sum of fractions
time limit per test
1 second
memory limit per test
64 megabytes
input
standard input
output
standard output

Once Maxim Vitalievich decided to deal with ordinary fractions. After quite a long study of the theory, he came up with an entertaining problem. Given the following equation:

$$$$$$ \frac{1}{a} + \frac{1}{b} = \frac{c}{k} $$$$$$

It is necessary to determine for a given integer $$$k$$$ the number of triplets of positive integers $$$a$$$, $$$b$$$ and $$$c$$$ that are the solution of this equation such that $$$a \le b$$$.

Maksim Vitalievich solved this problem for a given number $$$k$$$ and now he is wondering at what $$$k$$$ ($$$1 \le k \le r$$$) the number of solutions will be maximum.

Input

The single line contains a single integer $$$r$$$ — the right bound for the number $$$k$$$.

$$$$$$ 1 \le r \le 10^9 $$$$$$

Output

In a single line print two space-separated integers $$$k$$$ and $$$s$$$ ($$$1 \le k \le r$$$) — the value at which the largest number of solutions and the number of solutions for the number $$$k$$$ are achieved.

If there are several solutions, then print the solution where $$$k$$$ is the smallest.

Examples
Input
3
Output
3 7
Input
5
Output
4 10
Note

In the first example, for $$$k = 3$$$ there are the following solutions:

$$$(1, 1, 6)$$$, $$$(2, 2, 3)$$$, $$$(3, 3, 2)$$$, $$$(6, 6, 1)$$$, $$$(1, 3, 4)$$$, $$$(2, 6, 2)$$$, $$$(4, 12, 1)$$$.