Problem Statement

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.