#### Registered Users Only

Please login to utilize this feature.

Do note that this website only supports submissions in C++.

### 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:

Nc_{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

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 100 | 36 | 1s | 256MB | Minimum |

2 | 0 | 3 | 1s | 256MB | Minimum |

### Judge Compile Command

g++-7 ans.cpp -o sortedandsorted -Wall -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512