Sorted and Sorted

AtCoder

IDarc097_c

Time2000ms

Memory256MB

Difficulty—

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

Samples

Input #1

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

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 $2$.

Input #2

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

Output #2

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

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Sorted and Sorted",
    "description": {
      "content": "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 ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc097_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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 ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments