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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.util.Arrays;

class SegmentTreeRSQ {
  public int M, H, N;
  public long[] st;
  public long[] plus;

  public SegmentTreeRSQ(int n) {
    N = n;
    M = Integer.highestOneBit(Math.max(N - 1, 1)) << 2;
    H = M >>> 1;
    st = new long[M];
    plus = new long[H];
  }

  public SegmentTreeRSQ(int[] a) {
    N = a.length;
    M = Integer.highestOneBit(Math.max(N - 1, 1)) << 2;
    H = M >>> 1;
    st = new long[M];
    plus = new long[H];
    for (int i = 0; i < N; i++) {
      st[H + i] = a[i];
    }
    for (int i = (M >> 1) - 1; i >= 1; i--) {
      propagate(i);
    }
  }

  public void add(int pos, int v) {
    for (int i = H + pos; i >= 1; i >>>= 1) {
      st[i] += v;
    }
  }

  private void propagate(int i) {
    int count = H / Integer.highestOneBit(i);
    st[i] = st[2 * i] + st[2 * i + 1] + plus[i] * count;
  }

  public void add(int l, int r, int v) {
    if (l < r)
      add(l, r, v, 0, H, 1);
  }

  private void add(int l, int r, int v, int cl, int cr, int cur) {
    if (cur >= H) {
      st[cur] += v;
    } else if (l <= cl && cr <= r) {
      plus[cur] += v;
      propagate(cur);
    } else {
      int mid = cl + cr >>> 1;
      if (cl < r && l < mid) {
        add(l, r, v, cl, mid, 2 * cur);
      }
      if (mid < r && l < cr) {
        add(l, r, v, mid, cr, 2 * cur + 1);
      }
      propagate(cur);
    }
  }

  private long gsum;

  public long sum(int l, int r) {
    gsum = 0;
    sum(l, r, 0, H, 1);
    return gsum;
  }

  private void sum(int l, int r, int cl, int cr, int cur) {
    if (l <= cl && cr <= r) {
      gsum += st[cur];
    } else {
      int mid = cl + cr >>> 1;
      if (cl < r && l < mid) {
        sum(l, r, cl, mid, 2 * cur);
      }
      if (mid < r && l < cr) {
        sum(l, r, mid, cr, 2 * cur + 1);
      }
      gsum += plus[cur] * (Math.min(r, cr) - Math.max(l, cl));
    }
  }
}


public class Main {

  private static void solve() {
    int n = ni();
    int[][] p = new int[2 * n][2];
    for (int i = 0; i < 2 * n; i++) {
      p[i][0] = ns()[0] == 'W' ? 0 : 1;
      p[i][1] = ni() - 1;
    }

    int[][] dp = new int[n + 1][n + 1];
    int[][] inv = new int[2][n];
    for (int i = 0; i < n * 2; i++) {
      inv[p[i][0]][p[i][1]] = i;
    }

    SegmentTreeRSQ st1 = new SegmentTreeRSQ(n * 2);
    SegmentTreeRSQ st2 = new SegmentTreeRSQ(n * 2);

    for (int[] v : dp)
      Arrays.fill(v, Integer.MAX_VALUE / 10);
    dp[0][0] = 0;

    for (int i = 0; i <= n; i++) {
      if (i > 0) {
        Arrays.fill(st2.plus, 0);
        Arrays.fill(st2.st, 0);

        for (int j = 0; j <= n; j++) {
          if (j > 0)
            st2.add(inv[1][j - 1], 1);
          int x = inv[0][i - 1];
          x -= (int) st1.sum(0, inv[0][i - 1]);
          x -= (int) st2.sum(0, inv[0][i - 1]);
          dp[i][j] = Math.min(dp[i][j], dp[i - 1][j] + x);
        }
        st1.add(inv[0][i - 1], 1);
      }

      Arrays.fill(st2.plus, 0);
      Arrays.fill(st2.st, 0);
      for (int j = 1; j <= n; j++) {
        st2.add(inv[1][j - 1], 1);
        int x = inv[1][j - 1];
        x -= (int) st1.sum(0, inv[1][j - 1]);
        x -= (int) st2.sum(0, inv[1][j - 1]);
        dp[i][j] = Math.min(dp[i][j], dp[i][j - 1] + x);
      }
    }
    System.out.println(dp[n][n]);
  }



  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}