Enter-View is a linear, street-like country. By linear, we mean all the cities of the country are placed on a single straight line - the -axis. Thus every city's position can be defined by a single coordinate, , the distance from the left borderline of the country. You can treat all cities as single points.

Unfortunately, the dictator of telecommunication of EV (Mr. S. Treat Jr.) doesn't know anything about the modern telecom technologies, except for peer-to-peer connections. Even worse, his thoughts on peer-to-peer connections are extremely faulty: he believes that, if people are living in city , there must be at least cables from city to every other city of EV - this way he can guarantee no congestion will ever occur!

Mr. Treat hires you to find out how much cable they need to implement this telecommunication system, given the coordination of the cities and their respective population.

Note that The connections between the cities can be shared. Look at the example for the detailed explanation.

Input Format

A number is given in the first line and then comes blocks, each representing a scenario.

Each scenario consists of three lines. The first line indicates the number of cities (N). The second line indicates the coordinates of the N cities. The third line contains the population of each of the cities. The cities needn't be in increasing order in the input.

Output Format

For each scenario of the input, write the length of cable needed in a single line modulo .

Constraints

Border to border length of the country

Sample Input

2  
3  
1 3 6  
10 20 30  
5  
5 55 555 55555 555555  
3333 333 333 33 35

Sample Output

280  
463055586