Problem:
Score : 600 points

Problem Statement

There are N points in a two-dimensional plane. The initial coordinates of the i-th point are (x_i, y_i). Now, each point starts moving at a speed of 1 per second, in a direction parallel to the x- or y- axis. You are given a character d_i that represents the specific direction in which the i-th point moves, as follows:

If d_i = R, the i-th point moves in the positive x direction;

If d_i = L, the i-th point moves in the negative x direction;

If d_i = U, the i-th point moves in the positive y direction;

If d_i = D, the i-th point moves in the negative y direction.

You can stop all the points at some moment of your choice after they start moving (including the moment they start moving).
Then, let x_{max} and x_{min} be the maximum and minimum among the x-coordinates of the N points, respectively. Similarly, let y_{max} and y_{min} be the maximum and minimum among the y-coordinates of the N points, respectively.

Find the minimum possible value of (x_{max} - x_{min}) \times (y_{max} - y_{min}) and print it.

Constraints

1 \leq N \leq 10^5

-10^8 \leq x_i,\ y_i \leq 10^8

x_i and y_i are integers.

d_i is R, L, U, or D.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1 d_1
x_2 y_2 d_2
.
.
.
x_N y_N d_N

Output

Print the minimum possible value of (x_{max} - x_{min}) \times (y_{max} - y_{min}).

The output will be considered correct when its absolute or relative error from the judge's output is at most 10^{-9}.

Sample Input 1

2
0 3 D
3 0 L

Sample Output 1

0

After three seconds, the two points will meet at the origin. The value in question will be 0 at that moment.

Sample Input 2

5
-7 -10 U
7 -6 U
-8 7 D
-3 3 D
0 -6 R

Sample Output 2

97.5

The answer may not be an integer.

Sample Input 3

20
6 -10 R
-4 -9 U
9 6 D
-3 -2 R
0 7 D
4 5 D
10 -10 U
-1 -8 U
10 -6 D
8 -5 U
6 4 D
0 3 D
7 9 R
9 -4 R
3 10 D
1 9 U
1 -6 U
9 -8 R
6 7 D
7 -3 D

Sample Output 3

273

Solution in Scala (2.11.7) (judge verdict: Wrong Answer)

object Main {
  import java.io.{BufferedReader, InputStream, InputStreamReader}
  import java.util.StringTokenizer
  import scala.reflect.ClassTag

  def main(args: Array[String]): Unit = {
    val out = new java.io.PrintWriter(System.out)
    new Main(out, new InputReader(System.in)).solve()
    out.flush()
  }

  private val oj = System.getenv("ATCODER_DEBUG") == null
  def DEBUG(f: => Unit): Unit = {
    if (!oj){ f }
  }
  def debug(as: Array[Boolean]): Unit = if (!oj){ debug(as.map(x => if(x) "1" else "0").mkString) }
  def debug(as: Array[Int]): Unit = if (!oj){ debug(as.mkString(" ")) }
  def debug(as: Array[Long]): Unit =if (!oj){ debug(as.mkString(" ")) }
  def debugDim(m: Array[Array[Long]]): Unit = if (!oj){
    REP(m.length) { i =>
      debug(m(i))
    }
  }
  def debugDimFlip(m: Array[Array[Long]]): Unit = if (!oj){
    REP(m(0).length) { j =>
      REP(m.length) { i =>
        System.err.print(m(i)(j))
        System.err.print(" ")
      }
      System.err.println()
    }
  }
  def debug(s: => String): Unit = DEBUG {
    System.err.println(s)
  }
  def debugL(num: => Long): Unit = DEBUG {
    System.err.println(num)
  }

  class InputReader(val stream: InputStream) {
    private val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    private var tokenizer: StringTokenizer = _

    def next(): String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = Integer.parseInt(next())
    def nextLong(): Long = java.lang.Long.parseLong(next())
    def nextChar(): Char = next().charAt(0)

    def ni(): Int = nextInt()
    def nl(): Long = nextLong()
    def nc(): Char = nextChar()
    def ns(): String = next()
    def ns(n: Int): Array[Char] = ns().toCharArray
    def na(n: Int, offset: Int = 0): Array[Int] = map(n)(_ => ni() + offset)
    def na2(n: Int, offset: Int = 0): (Array[Int], Array[Int]) = {
      val A1, A2 = Array.ofDim[Int](n)
      REP(n) { i =>
        A1(i) = ni() + offset
        A2(i) = ni() + offset
      }
      (A1, A2)
    }
    def nm(n: Int, m: Int): Array[Array[Int]] = {
      val A = Array.ofDim[Int](n, m)
      REP(n) { i =>
        REP(m) { j =>
          A(i)(j) = ni()
        }
      }
      A
    }
    def nal(n: Int): Array[Long] = map(n)(_ => nl())
    def nm_c(n: Int, m: Int): Array[Array[Char]] = map(n) (_ => ns(m))
  }

  def REP(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = offset
    val N = n + offset
    while(i < N) { f(i); i += 1 }
  }
  def REP_r(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = n - 1 + offset
    while(i >= offset) { f(i); i -= 1 }
  }
  def TO(from: Int, to: Int)(f: Int => Unit): Unit = {
    REP(to - from + 1, from) { i =>
      f(i)
    }
  }
  def map[@specialized A: ClassTag](n: Int, offset: Int = 0)(f: Int => A): Array[A] = {
    val res = Array.ofDim[A](n)
    REP(n)(i => res(i) = f(i + offset))
    res
  }

  def sumL(as: Array[Int]): Long = {
    var s = 0L
    REP(as.length)(i => s += as(i))
    s
  }
  def cumSum(as: Array[Int]): Array[Long] = {
    val cum = Array.ofDim[Long](as.length + 1)
    REP(as.length) { i =>
      cum(i + 1) = cum(i) + as(i)
    }
    cum
  }
}

class Main(out: java.io.PrintWriter, sc: Main.InputReader) {
  import sc._
  import Main._
  import java.util.Arrays.sort

  import scala.collection.mutable
  import math.{abs, max, min}
  import mutable.ArrayBuffer

  val INF: Int = 1e9.toInt

  class Pair {
    var min: Int = INF
    var max: Int = -INF
    def empty = min == INF
    def nonEmpty = min != INF
  }
  case class Axis(L: Pair, R: Pair, UD: Pair)

  // toIntとか+7とかするならvalにしろ
  @inline private def MOD = 1000000007

  def solve(): Unit = {
    val N = ni()
    val X, Y: Axis = Axis(new Pair, new Pair, new Pair)

    def setMinMax(v: Int, pair: Pair): Unit = {
      pair.max = max(pair.max, v)
      pair.min = min(pair.min, v)
    }

    REP(N) { _ =>
      val x, y = ni()
      val d = nc()
      d match {
        case 'R' =>
          setMinMax(x, X.R)
          setMinMax(y, Y.UD)

        case 'L' =>
          setMinMax(x, X.L)
          setMinMax(y, Y.UD)

        // Yの<-に対応させる
        case 'D' =>
          setMinMax(x, X.UD)
          setMinMax(y, Y.L)

        // Yの->に対応させる
        case 'U' =>
          setMinMax(x, X.UD)
          setMinMax(y, Y.R)
      }
    }

    val D = 1e-10
    val E = 1e-14

    def len(p: Double, ax: Axis) = {
      val ms = min(ax.UD.min.toDouble, min(ax.R.min + p, ax.L.min - p))
      val mx = max(ax.UD.max.toDouble, max(ax.R.max + p, ax.L.max - p))
      mx - ms
    }

    def f(p: Double): Double = {
      debug(s"xlen:${len(p, X)} ylen:${len(p, Y)}")
      len(p, X) * len(p, Y)
    }

    def test(p: Double): Boolean = {
      debug(s"p:$p ${f(p + D)} ${f(p)}")
      f(p + D) - f(p) > E
    }

    def findMin(ms: Double, mx: Double): Double = {
      var l = ms
      var r = mx
      while(abs(r - l) > E) {
        val med = (l + r) / 2
        if (test(med)) r = med
        else l = med
      }
      r
    }

    def points(ax: Axis): Seq[Int] = {
      val p1 = Seq(ax.L.min - ax.UD.min).filter(ax.UD.nonEmpty && ax.L.nonEmpty && _ > 0)
      val p2 = Seq(ax.UD.min - ax.R.min).filter(ax.UD.nonEmpty && ax.R.nonEmpty && _ > 0)
      val p3 = Seq(ax.L.max - ax.UD.max).filter(ax.UD.nonEmpty && ax.L.nonEmpty && _ > 0)
      val p4 = Seq(ax.UD.max - ax.R.max).filter(ax.UD.nonEmpty && ax.R.nonEmpty && _ > 0)
      val p5 = Seq(ax.L.min - ax.R.max).filter(ax.UD.empty && ax.L.nonEmpty && ax.R.nonEmpty && _ > 0)
      p1 ++ p2 ++ p3 ++ p4  ++ p5
    }

    val P = Seq(0) ++ (points(X) ++ points(Y)).distinct.sorted
    var ans = 1e18
    REP(P.length - 1) { i =>
      ans = min(ans, f(findMin(P(i), P(i + 1))))
    }

    out.println(f"$ans%.9f")
  }
}