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: Accepted)

import sys
input=sys.stdin.readline
sys.setrecursionlimit(10 ** 6)

def main():
    inf = 5000
    n = int(input()[:-1])
    # iより前に色cのj以上が何個あるかがcnts[c][i][j]
    cnts = [[[0] * (n + 1) for _ in range(2 * n + 1)] for __ in range(2)]
    pos = [[0] * n for _ in range(2)]
    for i in range(n * 2):
        c, a = input().split()
        c = (c == "W") * 1
        a = int(a) - 1
        pos[c][a] = i
        for cc in range(2):
            for j in range(n):
                if c == cc and a >= j:
                    cnts[cc][i + 1][j] = cnts[cc][i][j] + 1
                else:
                    cnts[cc][i + 1][j] = cnts[cc][i][j]
    #    for x in cnts:
    #        print(x)
    #    print(pos)

    dp = [[inf] * (n + 1) for _ in range(n + 1)]
    dp[0][0] = 0
    for w in range(1, n + 1):
        i = pos[1][w - 1]
        dp[0][w] = dp[0][w - 1] + cnts[0][i][0] + cnts[1][i][w - 1]
    for b in range(1, n + 1):
        i = pos[0][b - 1]
        dp[b][0] = dp[b - 1][0] + cnts[0][i][b - 1] + cnts[1][i][0]
    for b in range(1, n + 1):
        for w in range(1, n + 1):
            bi = pos[0][b - 1]
            wi = pos[1][w - 1]
            dp[b][w] = min(dp[b - 1][w] + cnts[0][bi][b - 1] + cnts[1][bi][w],
                           dp[b][w - 1] + cnts[0][wi][b] + cnts[1][wi][w - 1])
    print(dp[n][n])

main()