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 LuaJIT (2.0.4) (judge verdict: Accepted)

local mma, mmi = math.max, math.min
local n = io.read("*n", "*l")
local t = {}
local tmap = {}
for i = 1, 2 * n do tmap[i] = 0 end
for i = 1, 2 * n do
  local str = io.read()
  local tp, num = str:match("(%w) (%d+)")
  num = tonumber(num)
  if tp == "B" then num = num + n end
  t[i] = num
  tmap[num] = i
end

local wcnt, bcnt = {}, {}
for i = 1, n do
  wcnt[i] = {}
  bcnt[i] = {}
  local wc, bc = 0, 0
  for j = 1, 2 * n do
    if t[j] <= i then
      wc = wc + 1
    end
    if n < t[j] and t[j] - n <= i then
      bc = bc + 1
    end
    wcnt[i][j] = wc
    bcnt[i][j] = bc
  end
end

local d = {}
for i = 1, n + 1 do
  d[i] = {}
  for j = 1, n + 1 do
    d[i][j] = 1000000007
  end
end
d[1][1] = 0
for j = 1, n do
  d[1][j + 1] = d[1][j] + tmap[j] - wcnt[j][tmap[j]]
end
for i = 1, n do
  d[i + 1][1] = d[i][1] + tmap[n + i] - bcnt[i][tmap[n + i]]
  for j = 1, n do
    local sub1 = wcnt[j][tmap[n + i]]
    local sub2 = bcnt[i][tmap[n + i]]

    local sub3 = wcnt[j][tmap[j]]
    local sub4 = bcnt[i][tmap[j]]
    d[i + 1][j + 1] = mmi(d[i][j + 1] + tmap[n + i] - sub1 - sub2, d[i + 1][j] + tmap[j] - sub3 - sub4)
  end
end
print(d[n + 1][n + 1])