Problem:
Score : 1000 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

Snuke received N intervals as a birthday present.
The i-th interval was [-L_i, R_i].
It is guaranteed that both L_i and R_i are positive.
In other words, the origin is strictly inside each interval.

Snuke doesn't like overlapping intervals, so he decided to move some intervals.
For any positive integer d, if he pays d dollars, he can choose one of the intervals and move it by the distance of d.
That is, if the chosen segment is [a, b], he can change it to either [a+d, b+d] or [a-d, b-d].

He can repeat this type of operation arbitrary number of times.
After the operations, the intervals must be pairwise disjoint (however, they may touch at a point).
Formally, for any two intervals, the length of the intersection must be zero.

Compute the minimum cost required to achieve his goal.

Constraints

1 ≤ N ≤ 5000

1 ≤ L_i, R_i ≤ 10^9

All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N
L_1 R_1
:
L_N R_N

Output

Print the minimum cost required to achieve his goal.

Sample Input 1

4
2 7
2 5
4 1
7 5

Sample Output 1

22

One optimal solution is as follows:

Move the interval [-2, 7] to [6, 15] with 8 dollars

Move the interval [-2, 5] to [-1, 6] with 1 dollars

Move the interval [-4, 1] to [-6, -1] with 2 dollars

Move the interval [-7, 5] to [-18, -6] with 11 dollars

The total cost is 8 + 1 + 2 + 11 = 22 dollars.

Sample Input 2

20
97 2
75 25
82 84
17 56
32 2
28 37
57 39
18 11
79 6
40 68
68 16
40 63
93 49
91 10
55 68
31 80
57 18
34 28
76 55
21 80

Sample Output 2

7337

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Debug;
using SB = System.Text.StringBuilder;
using Number = System.Int64;
using System.Numerics;
using static System.Math;
namespace Program {
    public class Solver {
        Random rnd = new Random(0);
        public void Solve() {
            var n = ri;

            var a = Enumerate(n, x => new long[] { rl, rl }).ToList();
            if (n % 2 == 0) { n++; a.Add(new long[] { 0, 0 }); }
            a.Sort((l, r) => (l[0] + l[1]).CompareTo(r[0] + r[1]));
            a.Reverse();
            //左側に動かすコスト Σi*Len_{i} + Σr_i
            //右側に動かすコスト Σi*Len_{i} + Σl_i

            //すでに i 個左に置かれていて，中心に置いたかどうか
            var dp = new long[n + 5, 2];
            for (int i = 0; i < n + 5; i++)
                for (int j = 0; j < 2; j++)
                    dp[i, j] = INF;
            dp[0, 0] = 0;
            var cnt = 0;
            foreach (var x in a)
            {
                var l = x[0];
                var r = x[1];
                var len = x[0] + x[1];
                Debug.WriteLine(len);
                var next = new long[n + 5, 2];
                for (int i = 0; i < n + 5; i++)
                    for (int j = 0; j < 2; j++)
                        next[i, j] = INF;
                for (int j = 0; j < 2; j++)
                    for (int i = 0; i + j <= cnt; i++)
                    {
                        var k = cnt - j - i;
                        //left
                        next[i + 1, j] = Math.Min(next[i + 1, j], dp[i, j] + i * len + r);
                        //right
                        next[i, j] = Math.Min(next[i, j], dp[i, j] + k * len + l);
                        //center
                        if (j == 0) next[i, j + 1] = Math.Min(next[i, j + 1], dp[i, j] + len * (n - 1));
                    }
                cnt++;
                dp = next;
            }
            Console.WriteLine(dp[(n - 1) / 2, 1]);
        }
        const long INF = 1L << 60;
        static int[] dx = { -1, 0, 1, 0 };
        static int[] dy = { 0, 1, 0, -1 };

        int ri { get { return sc.Integer(); } }
        long rl { get { return sc.Long(); } }
        double rd { get { return sc.Double(); } }
        string rs { get { return sc.Scan(); } }
        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());

        static T[] Enumerate<T>(int n, Func<int, T> f) {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f(i);
            return a;
        }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
    }
}

#region main
static class Ex {
    static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }

    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
        return string.Join(st, ie);
    }

    static public void Main() {
        Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Program.Solver();
        try
        {
            solver.Solve();
            Console.Out.Flush();
        }
        catch { }
    }
}
#endregion
#region Ex
namespace Program.IO {
    using System.IO;
    using System.Text;
    using System.Globalization;

    public class Printer: StreamWriter {
        public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
        public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
    }

    public class StreamScanner {
        public StreamScanner(Stream stream) { str = stream; }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }

        private byte read() {
            if (isEof) return 0;
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }

        public char Char() {
            byte b = 0;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }
        public string Scan() {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine() {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
        public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
        public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
}

#endregion