Problem:
Score : 700 points

Problem Statement

There are N bags, each containing two white balls. The i-th box contains two balls with integers x_i and y_i written on them, respectively.

For each of these bags, you will paint one of the balls red, and paint the other blue.

Afterwards, the 2N balls will be classified according to color.

Then, we will define the following:

R_{max}: the maximum integer written on a ball painted in red

R_{min}: the minimum integer written on a ball painted in red

B_{max}: the maximum integer written on a ball painted in blue

B_{min}: the minimum integer written on a ball painted in blue

Find the minimum possible value of (R_{max} - R_{min}) \times (B_{max} - B_{min}).

Constraints

1 ≤ N ≤ 200,000

1 ≤ x_i, y_i ≤ 10^9

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print the minimum possible value.

Sample Input 1

3
1 2
3 4
5 6

Sample Output 1

15

The optimal solution is to paint the balls with x_1, x_2, y_3 red, and paint the balls with y_1, y_2, x_3 blue.

Sample Input 2

3
1010 10
1000 1
20 1020

Sample Output 2

380

Sample Input 3

2
1 1
1000000000 1000000000

Sample Output 3

999999998000000001

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

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

    @inline private[this] final 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 = {
    var i = from
    while(i <= to) { f(i); i += 1 }
  }
  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

  // toIntとか+7とかするならvalにしろ
  final private[this] val MOD = 1000000007

  def solve(): Unit = {
    val n = ni()
    val (x, y) = na2(n)
    // red >= blue
    val red, blue = Array.ofDim[Int](n)
    REP(n) { i =>
      if (x(i) >= y(i)) {
        red(i) = x(i)
        blue(i) = y(i)
      } else {
        blue(i) = x(i)
        red(i) = y(i)
      }
    }

    val mx = red.max
    val ms = blue.min

    def calcMin: Int = {
      import java.util.Comparator
      val determined, ix = ArrayBuffer[Int]()
      REP(n) { i =>
        // red==mx && blue==msの場合は値を固定することができない
        if (red(i) == mx && blue(i) != ms) {
          determined += blue(i)
        } else if (blue(i) == ms && red(i) != mx) {
          determined += red(i)
        } else {
          ix += i
        }
      }

//      debug(determined.mkString(" "))
//      debug(ix.mkString(" "))
      val dms = determined.min
      val dmx = determined.max

      val nums = Array.ofDim[(Int, Int)](ix.length * 2)
      REP(ix.length) { i =>
        nums(i * 2) = (red(ix(i)), i)
        nums(i * 2 + 1) = (blue(ix(i)), i)
      }
      sort(nums, new Comparator[(Int, Int)] {
        override def compare(o1: (Int, Int), o2: (Int, Int)): Int = Integer.compare(o1._1, o2._1)
      })

      debug(s"dms:$dms dmx:$dmx")
      debug(nums.mkString(" "))

      var res = 1e9.toInt
      var r = -1
      var cnt = 0
      val flg = Array.ofDim[Int](n)
      REP(min(nums.length, ix.length + 1)) { l =>
        // [l, r] 最小になるようにする
        while(r + 1 < nums.length && cnt < ix.length) {
          r += 1
          flg(nums(r)._2) += 1
          if (flg(nums(r)._2) == 2) cnt += 1
        }
        debug(s"l:$l r:$r cnt:$cnt")
        debug(flg)

        if (cnt == ix.length) {
          res = min(res, max(nums(r)._1, dmx) - min(nums(l)._1, dms))
        }

        if (flg(nums(l)._2) == 2) cnt -= 1
        flg(nums(l)._2) -= 1
      }

      res
    }

    // red >= blue の状態ではri<->biを入れ替えても結果は悪くしかならない
    def diff = (red.max - red.min).toLong * (blue.max - blue.min)

    // r側でmin, maxを使うとして、b側が最小になる値
    def same = (mx - ms).toLong * calcMin
    out.println(min(same, diff))
  }
}