CF1466E Apollo versus Pan

原题

翻译

xjk:降智题。orz

$$\begin{array}{}\text{(1)}& \sum _{i=1}^n\sum _{j=1}^n\sum _{k=1}^n(x_i\mathrm{and}{x}_j)\times (x_j\mathrm{or}{x}_k)& =\sum _{i=1}^n\sum _{j=1}^n(x_i\mathrm{and}{x}_j)\times \sum _{k=1}^n(x_j\mathrm{or}{x}_k)\text{(2)}& & =\sum _{j=1}^n(\sum _{i=1}^n{x}_i\mathrm{and}{x}_j)\times (\sum _{k=1}^n{x}_j\mathrm{or}{x}_k)\end{array}$$

对于$x_i$按位求和，复杂度$O(n)$