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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

class Bit:
  def __init__(self,n):
    self.bl = n.bit_length()
    self.size = n
    self.tree = [0]*(n+1)
 
  def sum(self,i):
    s = 0
    while i > 0:
      s += self.tree[i]
      i -= i & -i
    return s

  def add(self,i,x):
    while i <= self.size:
      self.tree[i] += x
      i += i & -i
import sys
input = sys.stdin.readline
from copy import deepcopy
from collections import defaultdict
n = int(input())
ca = [input().rstrip() for i in range(2*n)]
dcw = defaultdict(int)
dcb = defaultdict(int)
for i in range(2*n):
  if ca[i][0] == "W":
    dcw[int(ca[i][2])] = i+1
  else:
    dcb[int(ca[i][2])] = i+1
dp = [[10**7 for i in range(n+1)] for j in range(n+1)]
dp[0][0] = 0
bit0 = Bit(2*n)
for i in range(n+1):
  if i:
    bit0.add(dcw[i],1)
  if i < n:
    dp[i+1][0] = dp[i][0]+dcw[i+1]-bit0.sum(dcw[i+1])-1
  bitc = deepcopy(bit0)
  for j in range(n+1):
    if j < n:
      dp[i][j+1] = min(dp[i][j+1],dp[i][j]+dcb[j+1]-bitc.sum(dcb[j+1])-1)
    if i < n:
      dp[i+1][j] = dp[i][j]+dcw[i+1]-bitc.sum(dcw[i+1])-1
    if j < n:
      bitc.add(dcb[j+1],1)
      #print(i,j,dc[bx],bitc.sum(dc[bx]))
print(dp[-1][-1])