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.