Manhattan Max Matching

Snuke 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.

Input

Input 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

Output

Print the maximum possible sum of the scores of the pairs.

Examples

Input

2 0 0 1 3 2 1 2 2 1 5 0 1

Output

8

Input

3 0 0 1 2 2 1 0 0 2 1 1 1 1 1 1 3 3 2

Output

16

Input

10 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

Output

45152033546

inputFormat

input are integers.

Input

Input 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

outputFormat

Output

Print the maximum possible sum of the scores of the pairs.

Examples

Input

2 0 0 1 3 2 1 2 2 1 5 0 1

Output

8

Input

3 0 0 1 2 2 1 0 0 2 1 1 1 1 1 1 3 3 2

Output

16

Input

10 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

Output

45152033546

样例

3
0 0 1
2 2 1
0 0 2
1 1 1
1 1 1
3 3 2

16