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)

class BIT
    def initialize(n)
        @n = n+1
        @dat = Array.new(@n+1, 0)
    end

    def sum(i)
        s = 0
        while i >= 0 do
            s += @dat[i]
            i = (i & (i + 1)) - 1
        end
        s
    end

    def add(i, x)
        while i <= @n do
            @dat[i] += x
            i |= i + 1
        end
    end
end


N = gets.to_i
cs, as = [], []
rev_b, rev_w = [], []
(2*N).times do |i|
    cs[i], as[i] = gets.split
    as[i] = as[i].to_i
    if cs[i] == 'B'
        rev_b[as[i]] = i
    else
        rev_w[as[i]] = i
    end
end

bit_b = BIT.new(N)
bit_w = BIT.new(N)
before_b = Array.new(2*N){Array.new(N, 0)}
before_w = Array.new(2*N){Array.new(N, 0)}
(2*N).times do |i|
    (1..N).each do |j|
        before_b[i][j] = bit_b.sum(j)
        before_w[i][j] = bit_w.sum(j)
    end
    if cs[i] == 'B'
        bit_b.add(as[i], 1)
    else
        bit_w.add(as[i], 1)
    end
end

# dp[b][w]
dp = Array.new(N+1){Array.new(N+1, 0)}
(1..(2*N)).each do |sum|
    lb = [0, sum - N].max
    ub = [sum, N].min
    (lb..ub).each do |b|
        w = sum - b
        cand = 10**10
        if b > 0
            pos = rev_b[b]
            d = dp[b-1][w] + (pos - before_b[pos][b-1] - before_w[pos][w])
            cand = d if cand > d
        end
        if w > 0
            pos = rev_w[w]
            d = dp[b][w-1] + (pos - before_b[pos][b] - before_w[pos][w-1])
            cand = d if cand > d
        end
        dp[b][w] = cand
    end
end
puts dp[N][N]