200972: [AtCoder]ARC097 E - Sorted and Sorted

Problem Statement

There are $2N$ balls, $N$ white and $N$ black, arranged in a row. The integers from $1$ through $N$ are written on the white balls, one on each ball, and they are also written on the black balls, one on each ball. The integer written on the $i$-th ball from the left ($1$ $≤$ $i$ $≤$ $2N$) is $a_i$, and the color of this ball is represented by a letter $c_i$. $c_i$ $=$ W represents the ball is white; $c_i$ $=$ B represents the ball is black.

Takahashi the human wants to achieve the following objective:

• For every pair of integers $(i,j)$ such that $1$ $≤$ $i$ $<$ $j$ $≤$ $N$, the white ball with $i$ written on it is to the left of the white ball with $j$ written on it.
• For every pair of integers $(i,j)$ such that $1$ $≤$ $i$ $<$ $j$ $≤$ $N$, the black ball with $i$ written on it is to the left of the black ball with $j$ written on it.

In order to achieve this, he can perform the following operation:

• Swap two adjacent balls.

Find the minimum number of operations required to achieve the objective.

Constraints

• $1$ $≤$ $N$ $≤$ $2000$
• $1$ $≤$ $a_i$ $≤$ $N$
• $c_i$ $=$ W or $c_i$ $=$ B.
• If $i$ $≠$ $j$, $(a_i,c_i)$ $≠$ $(a_j,c_j)$.

Input

Input is given from Standard Input in the following format:

$N$
$c_1$ $a_1$
$c_2$ $a_2$
$:$
$c_{2N}$ $a_{2N}$

Output

Print the minimum number of operations required to achieve the objective.

Sample Input 1

3
B 1
W 2
B 3
W 1
W 3
B 2

Sample Output 1

4

The objective can be achieved in four operations, for example, as follows:

• Swap the black $3$ and white $1$.
• Swap the white $1$ and white $2$.
• Swap the black $3$ and white $3$.
• Swap the black $3$ and black $2$.

Sample Input 2

4
B 4
W 4
B 3
W 3
B 2
W 2
B 1
W 1

Sample Output 2

18

Sample Input 3

9
W 3
B 1
B 4
W 1
B 5
W 9
W 2
B 6
W 5
B 3
W 8
B 9
W 7
B 2
B 8
W 4
W 6
B 7

Sample Output 3

41