Codeforces Round 624 (Div. 3) |
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Finished |

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data structures

divide and conquer

implementation

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F. Moving Points

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere 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).

Input

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.

Output

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).

Examples

Input

3 1 3 2 -100 2 3

Output

3

Input

5 2 1 4 3 5 2 2 2 3 4

Output

19

Input

2 2 1 -3 0

Output

0

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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