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sortedandsorted Batch , stdin/stdout

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sortedandsorted.html

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 ai, and the color of this ball is represented by a letter ci. ci = W represents the ball is white; ci = 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 ≤ ai ≤ N
  • ci = W or ci = B.
  • If i ≠ j, (ai,ci) ≠ (aj,cj).

Input

Input is given from Standard Input in the following format:

N
c1 a1
c2 a2
:
c2N a2N

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

AtCoder, Dynamic Programming

Subtasks and Limits

Subtask Score #TC Time Memory Scoring
1100361s256MBMinimum
2031s256MBMinimum

Judge Compile Command

g++-8 ans.cpp -o sortedandsorted -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512

Accepted Submissions

subIDUserTimeMax Time

Past Submissions

subIDUserTimeScore
mrJudge 09.05.20
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