Problem:
Score : 700 points

Problem Statement

Takahashi and Aoki will play a game with a number line and some segments.
Takahashi is standing on the number line and he is initially at coordinate 0.
Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).

The game has N steps. The i-th step proceeds as follows:

First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.

Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.

After N steps are performed, Takahashi will return to coordinate 0 and the game ends.

Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?

Constraints

1 ≤ N ≤ 10^5

-10^5 ≤ L_i < R_i ≤ 10^5

L_i and R_i are integers.

Input

Input is given from Standard Input in the following format:

N
L_1 R_1
:
L_N R_N

Output

Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above.
It is guaranteed that K is always an integer when L_i,R_i are integers.

Sample Input 1

3
-5 1
3 7
-4 -2

Sample Output 1

10

One possible sequence of actions of Takahashi and Aoki is as follows:

Aoki chooses the first segment. Takahashi moves from coordinate 0 to -4, covering a distance of 4.

Aoki chooses the third segment. Takahashi stays at coordinate -4.

Aoki chooses the second segment. Takahashi moves from coordinate -4 to 3, covering a distance of 7.

Takahashi moves from coordinate 3 to 0, covering a distance of 3.

The distance covered by Takahashi here is 14 (because Takahashi didn't move optimally).
It turns out that if both players move optimally, the distance covered by Takahashi will be 10.

Sample Input 2

3
1 2
3 4
5 6

Sample Output 2

12

Sample Input 3

5
-2 0
-2 0
7 8
9 10
-2 -1

Sample Output 3

34

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            AGC025.C();
        }

        class AGC025
        {
            public static void A()
            {
                var N = Read.Int();
                int sum = 0;
                while (N > 0)
                {
                    sum += N % 10;
                    N /= 10;
                }
                Console.WriteLine(sum == 1 ? 10 : sum);
            }
            public static void B()
            {
                var N = Read.Int();
                var A = Read.Long();
                var B = Read.Long();
                var K = Read.Long();

                var comb = Util.Combin(N + 1, Util.P);
                MOD sum = 0;
                for(int i = 0; i <= N; ++i)
                {
                    if ((K - i * A) % B == 0)
                    {
                        var j = (K - i * A) / B;
                        if (j < 0 || j>N) { continue; }
                        sum += comb(N, i) * comb(N, (int)j);
                    }
                }
                Console.WriteLine(sum.V);
            }
            public static void C()
            {
                var N = Read.Int();
                var LR = Read.TupleInt(N);
                var La = Enumerable.Range(0, N).OrderBy(i => -LR[i].Item1).ToArray();
                var Ra = Enumerable.Range(0, N).OrderBy(i => LR[i].Item2).ToArray();

                Func<int[], int[], List<int>> gen = (a1, a2) =>
                  {
                      List<int> list = new List<int>();
                      int idx1 = 0,idx2 = 0;
                      HashSet<int> hash = new HashSet<int>();
                      while (true)
                      {
                          while (hash.Contains(a1[idx1])) { idx1++; }
                          list.Add(a1[idx1]); hash.Add(a1[idx1]);
                          if (list.Count == N) { break; }
                          while (hash.Contains(a2[idx2])) { idx2++; }
                          list.Add(a2[idx2]); hash.Add(a2[idx2]);
                          if (list.Count == N) { break; }
                      }
                      return list;
                  };
                Func<List<int>, long> calc = (a) =>
                {
                    long total = 0;
                    int current = 0;
                    for(int i = 0; i < N; ++i)
                    {
                        var L = LR[a[i]].Item1;
                        var R = LR[a[i]].Item2;
                        if (current < L)
                        {
                            total += L - current;
                            current = L;
                        }
                        if (current > R)
                        {
                            total += current - R;
                            current = R;
                        }
                    }
                    total += Math.Abs(current);
                    return total;
                };
                Console.WriteLine(Math.Max(calc(gen(La, Ra)), calc(gen(Ra, La))));
            }
        }


        class Util
        {
            public static readonly long P = 998244353;
            public static long Inverse(long a, long p)
            {
                long b = p, c = 1, d = 0, e = 0, f = 0;
                while (b != 0)
                {
                    e = a / b;
                    f = b; b = a - e * b; a = f;
                    f = d; d = c - e * d; c = f;
                }
                c %= p;
                return c + (c < 0 ? p : 0);
            }
            public static long[] Facts(int n, long p)
            {
                var facts = new long[n + 1];
                facts[0] = 1;
                for (int i = 1; i <= n; ++i)
                {
                    facts[i] = (i * facts[i - 1]) % p;
                }
                return facts;
            }
            public static Func<int, int, long> Combin(int n, long P)
            {
                var fact = Facts(n, P);
                var inv = fact.Select(x => Inverse(x, P)).ToArray();
                return (N, M) =>
                {
                    if (N < 0 || N < M || M < 0) { return 0; }
                    return (((fact[N] * inv[M]) % P) * inv[N - M]) % P;
                };
            }
            public static long Power(long a, long n, long p)
            {
                long res = 1;
                long mult = a;
                for (int i = 0; i < 40; ++i)
                {
                    if ((n & ((long)1 << i)) > 0)
                    {
                        res = (res * mult) % p;
                    }
                    mult = (mult * mult) % p;
                }
                return res;
            }
        }
        struct MOD
        {
            public static long P = 998244353;
            public readonly long V;

            public MOD(long a) { this.V = a; }
            public static implicit operator MOD(long a) { return new MOD(a); }
            public static MOD operator +(MOD a, MOD b) { return new MOD((a.V + b.V) % P); }
            public static MOD operator -(MOD a, MOD b) { return new MOD((a.V - b.V + P) % P); }
            public static MOD operator *(MOD a, MOD b) { return new MOD((a.V * b.V) % P); }
            public static MOD operator /(MOD a, MOD b) { return new MOD((a.V * b.Inverse().V) % P); }
            public MOD Inverse() { return Util.Inverse(V, P); }
            public MOD Power(long n) { return Util.Power(V, n, P); }
            public override string ToString() { return V.ToString(); }
        }


        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new HashSet<int>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1]);
                    dict[ab[1]].Add(ab[0]);
                }
                return dict;
            }
            public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1], ab[2]);
                    dict[ab[1]].Add(ab[0], ab[2]);
                }
                return dict;
            }
        }
    }
}