Problem Statement

Snuke has 2N dogs, numbered 1 through 2N.
The cuteness of Dog i is a_i.
The color of Dog i is c_i, which is R, G, or B; R stands for red, G stands for green, and B stands for blue.
Snuke has N kennels, and wants to put two dogs in each kennel.
Note that this means each dog will be in exactly one kennel.
When he puts two dogs in the same kennel, it will cause some dissatisfaction in that kennel.
The level of dissatisfaction is represented as an integer. When Dogs i and j are in the same kennel, the dissatisfaction will be 0 if c_i = c_j and |a_i - a_j| otherwise.
Find the minimum possible total dissatisfaction when putting two dogs in each of the N kennels.

Input

Input is given from Standard Input in the following format:
N
a_{1} c_{1}
$\vdots$
a_{2N} c_{2N}

Output

Print the minimum possible total dissatisfaction when putting two dogs in each of the N kennels.

Constraints

• $1 \leq N \leq 10^{5}$
• $1 \leq a_i \leq 10^{15}$
• a_i is an integer.
• c_i is R, G, or B.

Sample Input 1

1
1 R
2 G

Sample Output 1

1

• Dog 1 has the cuteness of 1, and Dog 2 has the cuteness of 2.
• Since $c_1 \neq c_2$, the dissatisfaction will be 1.

Sample Input 2

1
1 B
2 B

Sample Output 2

0

• Dog 1 has the cuteness of 1, and Dog 2 has the cuteness of 2.
• Since c_1 = c_2, the dissatisfaction will be 0.

Sample Input 3

10
585 B
293 B
788 B
222 B
772 G
841 B
115 R
603 G
450 B
325 R
851 B
205 G
134 G
651 R
565 R
548 B
391 G
19 G
808 B
475 B

Sample Output 3

0

见题面 Input 部分

见题面 Output 部分