KOPC12A - K12 - Building Construction

Given N buildings of height h1, h2, h3 ... hn, the objective is to make every building has equal height. This can be done by removing bricks from a building or adding some bricks to a building. Removing a brick or adding a brick is done at certain cost which will be given along with the heights of the buildings. Find the minimal cost at which you can make the buildings look beautiful by re-constructing the buildings such that the N buildings satisfy 

h1 = h2 = h3 = ... = hn = k (k can be any number).

For convenience, all buildings are considered to be vertical piles of bricks, which are of same dimensions. 

Input

The first line of input contains an integer T which denotes number of test cases .This will be followed by 3 * T lines, 3 lines per test case. The first line of each test case contains an integer n and the  second line contains n integers which denotes the heights of the buildings [h1, h2, h3 ... hn] and the third line contains n integers [c1, c2, c3 ... cn] which denotes the cost of adding or removing one unit of brick from the corresponding building.

T <= 15; n <= 10000; 0 <= Hi <= 10000; 0 <= Ci <= 10000;

Output

The output must contain T lines each line corresponding to a testcase.

Example

Input:
1
3
1 2 3
10 100 1000

Output:
120

Added by:Radhakrishnan Venkataramani
Date:2012-01-31
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Own

hide comments
2012-04-02 22:56:11 Dejan Tomic
Wait, I think I understand. Does the sum of all heights has to be the same at the end? If the answer is NO then I understand everything now...
2012-04-02 21:37:02 Dejan Tomic
I just do not understand the test case. Why is the solution 120?

If all 3 buildings should be of height 2, the cost would be 1010 (removing a brick from the 3rd building + adding to 1st).

If we however want 2 buildings of height 3, this could be accomplished by removing the only brick from the 1st building and adding it to the 2nd. But that would cost 110, not 120.

So how would you explain the solution of 120?
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