
Score : 1200 points
Problem StatementSnuke is playing with red and blue balls, placing them on a two-dimensional plane.
First, he performed N operations to place red balls. In the i-th of these operations, he placed RC_i red balls at coordinates (RX_i,RY_i).
Then, he performed another N operations to place blue balls. In the i-th of these operations, he placed BC_i blue balls at coordinates (BX_i,BY_i).
The total number of red balls placed and the total number of blue balls placed are equal, that is, \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i. Let this value be S.
Snuke will now form S pairs of red and blue balls so that every ball belongs to exactly one pair.
Let us define the score of a pair of a red ball at coordinates (rx, ry) and a blue ball at coordinates (bx, by) as |rx-bx| + |ry-by|.
Snuke wants to maximize the sum of the scores of the pairs.
Help him by finding the maximum possible sum of the scores of the pairs.
Constraints
1 \leq N \leq 1000
0 \leq RX_i,RY_i,BX_i,BY_i \leq 10^9
1 \leq RC_i,BC_i \leq 10
\sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i
All values in input are integers.
InputInput is given from Standard Input in the following format:
N
RX_1 RY_1 RC_1
RX_2 RY_2 RC_2
\vdots
RX_N RY_N RC_N
BX_1 BY_1 BC_1
BX_2 BY_2 BC_2
\vdots
BX_N BY_N BC_N
OutputPrint the maximum possible sum of the scores of the pairs.
Sample Input 12
0 0 1
3 2 1
2 2 1
5 0 1
Sample Output 18
If we pair the red ball at coordinates (0,0) and the blue ball at coordinates (2,2), the score of this pair is |0-2| + |0-2|=4.
Then, if we pair the red ball at coordinates (3,2) and the blue ball at coordinates (5,0), the score of this pair is |3-5| + |2-0|=4.
Making these two pairs results in the total score of 8, which is the maximum result.
Sample Input 23
0 0 1
2 2 1
0 0 2
1 1 1
1 1 1
3 3 2
Sample Output 216
Snuke may have performed multiple operations at the same coordinates.
Sample Input 310
582463373 690528069 8
621230322 318051944 4
356524296 974059503 6
372751381 111542460 9
392867214 581476334 6
606955458 513028121 5
882201596 791660614 9
250465517 91918758 3
618624774 406956634 6
426294747 736401096 5
974896051 888765942 5
726682138 336960821 3
715144179 82444709 6
599055841 501257806 6
390484433 962747856 4
912334580 219343832 8
570458984 648862300 6
638017635 572157978 10
435958984 585073520 7
445612658 234265014 6
Sample Output 345152033546
