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: Wrong Answer)

require 'pp'
N = gets.chomp.to_i
N2 = N * 2
c = []
a = []
N2.times do |i|
  x, y = gets.chomp.split(" ")
  c[i] = x == "B"
  a[i] = y.to_i
end

# pp c, a

ans = 0

l = 0

b_next = 1
w_next = 1

while l < N2
  c_l = c[l]
  a_l = a[l]

  if c_l == nil
    l += 1
    next
  end

  if c_l && b_next == a_l
    l += 1
    b_next += 1
    next
  end
  if !c_l && w_next == a_l
    l += 1
    w_next += 1
    next
  end

  move = 0
  r = l + 1
  while r < N2
    move += 1 if c[r] != nil
    if c[r] != nil
      if c[r] && b_next == a[r]
        b_next += 1
        c[r] = nil
        break
      end
      if !c[r] && w_next == a[r]
        w_next += 1
        c[r] = nil
        break
      end
    end
    r += 1
  end

  ans += move

  # l += 1
end

puts ans