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.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;
using System.IO;
using System.Text;
using System.Diagnostics;

using static util;
using P = pair<int, int>;

using Binary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.ParameterExpression,
                           System.Linq.Expressions.BinaryExpression>;
using Unary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.UnaryExpression>;

class Program
{
    static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    static Scan sc = new Scan();
    // const int M = 1000000007;
    const int M = 998244353;
    const long LM = (long)1e18;
    const double eps = 1e-11;
    static readonly int[] dd = { 0, 1, 0, -1, 0 };
    const string dstring = "RDLU";
    static void Main()
    {
        int n = sc.Int;
        var r = new List<int>();
        var l = new List<int>();
        r.Add(0);
        l.Add(0);
        for (int i = 0; i < n; i++)
        {
            int a, b;
            sc.Multi(out a, out b);
            r.Add(a);
            l.Add(-b);
        }
        r.Sort();
        r.Reverse();
        l.Sort();
        l.Reverse();
        long ans = 0;
        for (int i = 0; i < r.Count && i < l.Count; i++)
        {
            if (r[i] + l[i] < 0) break;
            ans += r[i] + l[i];
        }
        Prt(ans * 2);
        sw.Flush();
    }

    static void DBG(string a) => Console.WriteLine(a);
    static void DBG<T>(IEnumerable<T> a) => DBG(string.Join(" ", a));
    static void DBG(params object[] a) => DBG(string.Join(" ", a));
    static void Prt(string a) => sw.WriteLine(a);
    static void Prt<T>(IEnumerable<T> a) => Prt(string.Join(" ", a));
    static void Prt(params object[] a) => Prt(string.Join(" ", a));
}
class pair<T, U> : IComparable<pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T v1;
    public U v2;
    public pair(T v1, U v2) {
        this.v1 = v1;
        this.v2 = v2;
    }
    public int CompareTo(pair<T, U> a) => v1.CompareTo(a.v1) != 0 ? v1.CompareTo(a.v1) : v2.CompareTo(a.v2);
    public override string ToString() => v1 + " " + v2;
}
static class util
{
    public static pair<T, T> make_pair<T>(this IList<T> l) where T : IComparable<T> => make_pair(l[0], l[1]);
    public static pair<T, U> make_pair<T, U>(T v1, U v2) where T : IComparable<T> where U : IComparable<U> => new pair<T, U>(v1, v2);
    public static T sqr<T>(T a) => Operator<T>.Multiply(a, a);
    public static T Max<T>(params T[] a) => a.Max();
    public static T Min<T>(params T[] a) => a.Min();
    public static bool inside(int i, int j, int h, int w) => i >= 0 && i < h && j >= 0 && j < w;
    public static void swap<T>(ref T a, ref T b) { var t = a; a = b; b = t; }
    public static void swap<T>(this IList<T> a, int i, int j) { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a) {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
static class Operator<T>
{
    static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x");
    static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y");
    public static readonly Func<T, T, T> Add = Lambda(Expression.Add);
    public static readonly Func<T, T, T> Subtract = Lambda(Expression.Subtract);
    public static readonly Func<T, T, T> Multiply = Lambda(Expression.Multiply);
    public static readonly Func<T, T, T> Divide = Lambda(Expression.Divide);
    public static readonly Func<T, T> Plus = Lambda(Expression.UnaryPlus);
    public static readonly Func<T, T> Negate = Lambda(Expression.Negate);
    public static Func<T, T, T> Lambda(Binary op) => Expression.Lambda<Func<T, T, T>>(op(x, y), x, y).Compile();
    public static Func<T, T> Lambda(Unary op) => Expression.Lambda<Func<T, T>>(op(x), x).Compile();
}

class Scan
{
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public string Str => Console.ReadLine().Trim();
    public pair<T, U> Pair<T, U>() where T : IComparable<T> where U : IComparable<U>
    { T a; U b; Multi(out a, out b); return new pair<T, U>(a, b); }
    public int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public double[] DoubleArr => StrArr.Select(double.Parse).ToArray();
    public string[] StrArr => Str.Split(new []{' '}, System.StringSplitOptions.RemoveEmptyEntries);
    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    T cv<T>(string s) => eq<T, int>()    ? ct<T, int>(int.Parse(s))
                       : eq<T, long>()   ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, char>()   ? ct<T, char>(s[0])
                                         : ct<T, string>(s);
    public void Multi<T>(out T a) => a = cv<T>(Str);
    public void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
    public void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]); }
}
static class mymath
{
    public static long Mod = 1000000007;
    public static bool isprime(long a) {
        if (a < 2) return false;
        for (long i = 2; i * i <= a; i++) if (a % i == 0) return false;
        return true;
    }
    public static bool[] sieve(int n) {
        var p = new bool[n + 1];
        for (int i = 2; i <= n; i++) p[i] = true;
        for (int i = 2; i * i <= n; i++) if (p[i]) for (int j = i * i; j <= n; j += i) p[j] = false;
        return p;
    }
    public static List<int> getprimes(int n) {
        var prs = new List<int>();
        var p = sieve(n);
        for (int i = 2; i <= n; i++) if (p[i]) prs.Add(i);
        return prs;
    }
    public static long[][] E(int n) {
        var ret = new long[n][];
        for (int i = 0; i < n; i++) { ret[i] = new long[n]; ret[i][i] = 1; }
        return ret;
    }
    public static double[][] dE(int n) {
        var ret = new double[n][];
        for (int i = 0; i < n; i++) { ret[i] = new double[n]; ret[i][i] = 1; }
        return ret;
    }
    public static long[][] pow(long[][] A, long n) {
        if (n == 0) return E(A.Length);
        var t = pow(A, n / 2);
        if ((n & 1) == 0) return mul(t, t);
        return mul(mul(t, t), A);
    }
    public static double[][] pow(double[][] A, long n) {
        if (n == 0) return dE(A.Length);
        var t = pow(A, n / 2);
        if ((n & 1) == 0) return mul(t, t);
        return mul(mul(t, t), A);
    }
    public static double dot(double[] x, double[] y) {
        int n = x.Length;
        double ret = 0;
        for (int i = 0; i < n; i++) ret += x[i] * y[i];
        return ret;
    }
    public static long dot(long[] x, long[] y) {
        int n = x.Length;
        long ret = 0;
        for (int i = 0; i < n; i++) ret = (ret + x[i] * y[i]) % Mod;
        return ret;
    }
    public static int dot(int[] x, int[] y) {
        int n = x.Length;
        int ret = 0;
        for (int i = 0; i < n; i++) ret += x[i] * y[i];
        return ret;
    }
    public static T[][] trans<T>(T[][] A) {
        int n = A[0].Length, m = A.Length;
        var ret = new T[n][];
        for (int i = 0; i < n; i++) { ret[i] = new T[m]; for (int j = 0; j < m; j++) ret[i][j] = A[j][i]; }
        return ret;
    }
    public static double[] mul(double a, double[] x) {
        int n = x.Length;
        var ret = new double[n];
        for (int i = 0; i < n; i++) ret[i] = a * x[i];
        return ret;
    }
    public static long[] mul(long a, long[] x) {
        int n = x.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = a * x[i] % Mod;
        return ret;
    }
    public static double[] mul(double[][] A, double[] x) {
        int n = A.Length;
        var ret = new double[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static long[] mul(long[][] A, long[] x) {
        int n = A.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static int[] mul(int[][] A, int[] x) {
        int n = A.Length;
        var ret = new int[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static double[][] mul(double a, double[][] A) {
        int n = A.Length;
        var ret = new double[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(a, A[i]);
        return ret;
    }
    public static long[][] mul(long a, long[][] A) {
        int n = A.Length;
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(a, A[i]);
        return ret;
    }
    public static double[][] mul(double[][] A, double[][] B) {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new double[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
        return ret;
    }
    public static long[][] mul(long[][] A, long[][] B) {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
        return ret;
    }
    public static int[][] mul(int[][] A, int[][] B) {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new int[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
        return ret;
    }
    public static long[] add(long[] x, long[] y) {
        int n = x.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = (x[i] + y[i]) % Mod;
        return ret;
    }
    public static int[] add(int[] x, int[] y) {
        int n = x.Length;
        var ret = new int[n];
        for (int i = 0; i < n; i++) ret[i] = x[i] + y[i];
        return ret;
    }
    public static long[][] add(long[][] A, long[][] B) {
        int n = A.Length;
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = add(A[i], B[i]);
        return ret;
    }
    public static double[] add(double[] x, double[] y) {
        int n = x.Length;
        var ret = new double[n];
        for (int i = 0; i < n; i++) ret[i] = (x[i] + y[i]) % Mod;
        return ret;
    }
    public static double[][] add(double[][] A, double[][] B) {
        int n = A.Length;
        var ret = new double[n][];
        for (int i = 0; i < n; i++) ret[i] = add(A[i], B[i]);
        return ret;
    }
    public static long pow(long a, long b) {
        if (a >= Mod) return pow(a % Mod, b);
        if (a == 0) return 0;
        if (b == 0) return 1;
        var t = pow(a, b / 2);
        if ((b & 1) == 0) return t * t % Mod;
        return t * t % Mod * a % Mod;
    }
    public static long inv(long a) => pow(a, Mod - 2);
    public static long gcd(long a, long b) {
        while (b > 0) { var t = a % b; a = b; b = t; } return a;
    }
    // a x + b y = gcd(a, b)
    public static long extgcd(long a, long b, out long x, out long y) {
        long g = a; x = 1; y = 0;
        if (b > 0) { g = extgcd(b, a % b, out y, out x); y -= a / b * x; }
        return g;
    }
    public static long lcm(long a, long b) => a / gcd(a, b) * b;

    static long[] facts;
    public static long[] setfacts(int n) {
        facts = new long[n + 1];
        facts[0] = 1;
        for (int i = 0; i < n; i++) facts[i + 1] = facts[i] * (i + 1) % Mod;
        return facts;
    }
    public static long comb(int n, int r) {
        if (n < 0 || r < 0 || r > n) return 0;
        if (n - r < r) r = n - r;
        if (r == 0) return 1;
        if (r == 1) return n;
        if (facts != null && facts.Length > n) return facts[n] * inv(facts[r]) % Mod * inv(facts[n - r]) % Mod;
        int[] numer = new int[r], denom = new int[r];
        for (int k = 0; k < r; k++) { numer[k] = n - r + k + 1; denom[k] = k + 1; }
        for (int p = 2; p <= r; p++) {
            int piv = denom[p - 1];
            if (piv > 1) {
                int ofst = (n - r) % p;
                for (int k = p - 1; k < r; k += p) { numer[k - ofst] /= piv; denom[k] /= piv; }
            }
        }
        long ret = 1;
        for (int k = 0; k < r; k++) if (numer[k] > 1) ret = ret * numer[k] % Mod;
        return ret;
    }
    public static long[][] getcombs(int n) {
        var ret = new long[n + 1][];
        for (int i = 0; i <= n; i++) {
            ret[i] = new long[i + 1];
            ret[i][0] = ret[i][i] = 1;
            for (int j = 1; j < i; j++) ret[i][j] = (ret[i - 1][j - 1] + ret[i - 1][j]) % Mod;
        }
        return ret;
    }
    // nC0, nC2, ..., nCn
    public static long[] getcomb(int n) {
        var ret = new long[n + 1];
        ret[0] = 1;
        for (int i = 0; i < n; i++) ret[i + 1] = ret[i] * (n - i) % Mod * inv(i + 1) % Mod;
        return ret;
    }
}