Title Description
Given a positive integer $ n $, seeking three mutually different positive integers $ x, y, z, $, such that $ \ frac {1} {x} + \ frac {1} {y} + \ frac { 1} {z} = \ frac {2} {n} $.
Input Format
A positive integer $ n $.
Output Format
Three positive integers $ x, y, z $, such as the title.
Sample
Sample input
2
Sample Output
2 3 6
Data range and tips
$2\leqslant n\leqslant 2^{32}-1$
Offers Special Judge
answer
If you see here, that you also dishes than I am.
After all, I gave you a sample ......
Find the law should also find out ......
You will be given $ \ Theta (n ^ 3) $ violence.
A little thought can find $ x, y $ launched the $ z $, $ \ Theta (n ^ 2) $ came out.
But the data range is clearly let $ \ Theta (1) $ (although the original title n \ leqslant {10} ^ 4 $).
You really dish, read here still think of $ \ Theta (1) $. . .
Well, I'll tell you, after all, I found the people than I dish ......
There is such a formula: $ \ frac {1} {n} - \ frac {1} {n + 1} = \ frac {1} {n \ times (n + 1)} $.
Then we move entries: $ \ frac {1} {n \ times (n + 1)} + \ frac {1} {n + 1} - \ frac {1} {n} = 0 $.
Sides while adding $ \ frac {2} {n} $: $ \ frac {1} {n} + \ frac {1} {n + 1} + \ frac {1} {n \ times (n + 1)} = \ frac {2} {n} $.
So we let $ x = n, y = n + 1, z = n \ times (n + 1) $ thousand million ......
See here, it is not that he is mentally retarded?
stop! ! !
Do not commit suicide! ! !
The author is not responsible! ! !