A13349 | Moving Points

There are $n$ points on a coordinate axis $OX$ . The $i$ -th point is located at the integer point $x_i$ and has a speed $v_i$ . It is guaranteed that no two points occupy the same coordinate. All $n$ points move with the constant speed, the coordinate of the $i$ -th point at the moment $t$ ( $t$ can be non-integer) is calculated as $x_i + t \cdot v_i$ .

Consider two points $i$ and $j$ . Let $d(i, j)$ be the minimum possible distance between these two points over any possible moments of time (even non-integer). It means that if two points $i$ and $j$ coincide at some moment, the value $d(i, j)$ will be $0$ .

Your task is to calculate the value $\sum\limits_{1 \le i < j \le n}$ $d(i, j)$ (the sum of minimum distances over all pairs of points).

The first line of the input contains one integer $n$ ( $2 \le n \le 2 \cdot 10^5$ ) — the number of points.

The second line of the input contains $n$ integers $x_1, x_2, \dots, x_n$ ( $1 \le x_i \le 10^8$ ), where $x_i$ is the initial coordinate of the $i$ -th point. It is guaranteed that all $x_i$ are distinct.

The third line of the input contains $n$ integers $v_1, v_2, \dots, v_n$ ( $-10^8 \le v_i \le 10^8$ ), where $v_i$ is the speed of the $i$ -th point.

Print one integer — the value $\sum\limits_{1 \le i < j \le n}$ $d(i, j)$ (the sum of minimum distances over all pairs of points).