AT_abc479_g [ABC479G] Tuning

You are given length- $ N $ integer sequences $ A=(A_1,A_2,\dots,A_N) $ and $ B=(B_1,B_2,\dots,B_N) $ . Consider length- $ N $ sequences of **rational numbers** $ c=(c_1,c_2,\dots,c_N) $ and $ d=(d_1,d_2,\dots,d_N) $ that satisfy the following condition. - $ (A_i+c_i)(B_j+d_j)=(A_j+c_j)(B_i+d_i) $ for all $ 1 \le i,j \le N $ . Find the minimum possible value of $ \displaystyle \sum_{i=1}^{N} \left ( |c_i|+|d_i| \right ) $ . It can be proved that the answer to this problem can be uniquely represented as an irreducible fraction $ p/q $ with a positive denominator and a non-negative numerator. Output these $ p $ and $ q $ .

The input is given from Standard Input in the following format: > $ N $ $ A_1 $ $ A_2 $ $ \dots $ $ A_N $ $ B_1 $ $ B_2 $ $ \dots $ $ B_N $

When the answer to this problem is represented as an irreducible fraction $ p/q $ with a positive denominator and a non-negative numerator, output it in the following format: > $ p $ $ q $

### Sample Explanation 1 For example, you can set $ c=(0,0,0),d=(0,-\frac{1}{4},0) $ , which achieves $ \sum_{i=1}^{N} \left ( |c_i|+|d_i| \right ) = \frac{1}{4} $ . Also, $ \sum_{i=1}^{N} \left ( |c_i|+|d_i| \right ) $ cannot be made smaller than this. ### Sample Explanation 2 If the answer is $ 0 $ , it is represented as $ 0/1 $ , so output `0 1`. ### Constraints - All input values are integers. - $ 2 \le N \le 2 \times 10^5 $ - $ |A_i|, |B_i| \le 10^6 $