Problem:
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 ≤ 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.

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

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

N = gets.to_i
balls = (0..1).map{ [] }
idx = (0..1).map{ {} }
(0...2*N).each{ |i|
  c,a = gets.split
  a = a.to_i
  ci = c == "B" ? 0 : 1
  balls[ci] << a
  balls[1 - ci] << 0
  idx[ci][a] = i
}

balls_larger_than = (0..1).map{ [] }
(0..N).each{ |v|
  (0..1).each{ |c|
    n = 0
    balls_larger_than[c] << (0...2*N).map{ |i|
      r = n
      n += 1 if balls[c][i] > v
      r
    }
  }
}

dp = (0..N).map{ Array.new(N+1,10**15) }
dp[0][0] = 0
(0..N).each{ |x|
  (0..N).each{ |y|
    if x < N
      ix = idx[0][x+1]
      v = dp[x][y] + balls_larger_than[0][x+1][ix] + balls_larger_than[1][y][ix]
      dp[x+1][y] = v if v < dp[x+1][y]
    end
    if y < N
      iy = idx[1][y+1]
      v = dp[x][y] + balls_larger_than[0][x][iy] + balls_larger_than[1][y+1][iy]
      dp[x][y+1] = v if v < dp[x][y+1]
    end
  }
}
p dp[-1][-1]