Score : $600$ points

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 ($1$ $\leq$ $i$ $\leq$ $2N$) 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 $1$ $\leq$ $i$ $<$ $j$ $\leq$ $N$, 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 $1$ $\leq$ $i$ $<$ $j$ $\leq$ $N$, 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

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

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.

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

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 $2$.

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

18

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

41