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)

class SegTreeMin
    attr_reader :dat
    def initialize(n_input, top=Float::INFINITY)
        @n_input = n_input
        @n = 1 << @n_input.to_s(2).length
        @top = top
        @dat = Array.new(2 * @n - 1, @top)
    end

    def update(k, a)
        k += @n - 1
        @dat[k] = a
        while k > 0 do
            k = (k - 1) / 2
            #@dat[k] = [@dat[2*k+1], @dat[2*k+2]].min
            @dat[k] = @dat[2*k+1]
            @dat[k] = @dat[2*k+2] if @dat[k] > @dat[2*k+2]
        end
    end

    # This works only when inserting larger value than all existing values
    def update_larger(k, a)
        k += @n - 1
        @dat[k] = a
        while k > 0 do
            k = (k - 1) / 2
            if @dat[k] <= a
                break
            else
                @dat[k] = a
            end
        end
    end

    # include a and b
    def min_between(a, b)
        query(a, b + 1, 0, 0, @n)
    end

    def query(a, b, k, l, r)
        return @top if r <= a || b <= l
        return @dat[k] if a <= l && r <= b
        vl = query(a, b, k * 2 + 1, l, (l + r) / 2)
        vr = query(a, b, k * 2 + 2, (l + r) / 2, r)
        #return [vl, vr].min
        return vl < vr ? vl : vr
    end
end



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
st_w = SegTreeMin.new(N, N+2)
st_b = SegTreeMin.new(N, N+2)
bit_w = BIT.new(N)
bit_b = BIT.new(N)
wp = []
bp = []
wcum = []
bcum = []
wcum_bit = BIT.new(2*N)
bcum_bit = BIT.new(2*N)

ans = 0
(2*N).times do |i|
    c, a = gets.chomp.split
    a = a.to_i - 1
    bcum[i] = i == 0 ? 0 : bcum[i-1]
    wcum[i] = i == 0 ? 0 : wcum[i-1]
    if c == 'B'
        bcum[i] += 1

        ans += bcum[i] - bit_b.sum(a) - 1
        bit_b.add(a, 1)

        left = st_b.min_between(a+1, N)
        if left != N + 2
            jumped_w = wcum_bit.sum(i) - wcum_bit.sum(left)
            ans += jumped_w
            bcum_bit.add(left, 1)
            st_b.update(a, left)
        else
            st_b.update(a, i)
            bcum_bit.add(i, 1)
        end

    else
        wcum[i] += 1

        ans += wcum[i] - bit_w.sum(a) - 1
        bit_w.add(a, 1)

        left = st_w.min_between(a+1, N)
        if left != N + 2
            jumped_b = bcum_bit.sum(i) - bcum_bit.sum(left)
            ans += jumped_b
            st_w.update(a, left)
            wcum_bit.add(left, 1)
        else
            st_w.update(a, i)
            wcum_bit.add(i, 1)
        end
    end
end
puts ans