Problem:
Score : 300 points

Problem Statement

There are N sightseeing spots on the x-axis, numbered 1, 2, ..., N.
Spot i is at the point with coordinate A_i.
It costs |a - b| yen (the currency of Japan) to travel from a point with coordinate a to another point with coordinate b along the axis.

You planned a trip along the axis.
In this plan, you first depart from the point with coordinate 0, then visit the N spots in the order they are numbered, and finally return to the point with coordinate 0.

However, something came up just before the trip, and you no longer have enough time to visit all the N spots, so you decided to choose some i and cancel the visit to Spot i.
You will visit the remaining spots as planned in the order they are numbered.
You will also depart from and return to the point with coordinate 0 at the beginning and the end, as planned.

For each i = 1, 2, ..., N, find the total cost of travel during the trip when the visit to Spot i is canceled.

Constraints

2 \leq N \leq 10^5

-5000 \leq A_i \leq 5000 (1 \leq i \leq N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print N lines.
In the i-th line, print the total cost of travel during the trip when the visit to Spot i is canceled.

Sample Input 1

3
3 5 -1

Sample Output 1

12
8
10

Spot 1, 2 and 3 are at the points with coordinates 3, 5 and -1, respectively.
For each i, the course of the trip and the total cost of travel when the visit to Spot i is canceled, are as follows:

For i = 1, the course of the trip is 0 \rightarrow 5 \rightarrow -1 \rightarrow 0 and the total cost of travel is 5 + 6 + 1 = 12 yen.

For i = 2, the course of the trip is 0 \rightarrow 3 \rightarrow -1 \rightarrow 0 and the total cost of travel is 3 + 4 + 1 = 8 yen.

For i = 3, the course of the trip is 0 \rightarrow 3 \rightarrow 5 \rightarrow 0 and the total cost of travel is 3 + 2 + 5 = 10 yen.

Sample Input 2

5
1 1 1 2 0

Sample Output 2

4
4
4
2
4

Sample Input 3

6
-679 -2409 -3258 3095 -3291 -4462

Sample Output 3

21630
21630
19932
8924
21630
19288

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

namespace AtCoder.ABC.C092
{
    using System;
    using System.Collections;
    using System.Collections.Generic;
    using System.Linq;
    using System.Numerics;
    using System.IO;

    using AtCoder.ABC.IO;

    public class Quest
    {
        public object Solve(Parser parser)
        {
            int n = parser.Integer();

            var red = parser.Take(n).Select(p => new Red()
            {
                x = p.Integer(),
                y = p.Integer(),
            }).OrderByDescending(r => r.y).ToArray();

            Blue[] blue = parser.Take(n).Select(p => new Blue()
            {
                x = p.Integer(),
                y = p.Integer(),
            }).OrderBy(b => b.x).ToArray();

            var g = new Graph();

            for (int i = 0; i < red.Length; i++)
            {
                g.AddEdge(0, 1 + i, 1);
                for (int j = 0; j < blue.Length; j++)
                {
                    if (IsFriend(red[i], blue[j]))
                    {
                        g.AddEdge(1 + i, 1 + j + red.Length, 1);
                    }
                }
            }

            for (int j = 0; j < blue.Length; j++)
            {
                g.AddEdge(1 + j + red.Length, 1 + red.Length + blue.Length, 1);
            }

            return g.MaximizeFlow(0, 1 + red.Length + blue.Length);
        }
        private static bool IsFriend(Red red, Blue blue)
        {
            return red.x < blue.x && red.y < blue.y;
        }
    }

    class Edge
    {
        public int To;
        public int Capacity;
        public int Reverse;
    }

    class Graph
    {
        private Dictionary<int, List<Edge>> m_edges;

        public Graph()
        {
            m_edges = new Dictionary<int, List<Edge>>();
        }


        public int MaximizeFlow(int s, int t)
        {
            int flow = 0;

            while (true)
            {
                bool[] used = Enumerable.Range(0, m_edges.Count)
                .Select(x => false).ToArray();

                int f = Dfs(s, t, int.MaxValue, used);
                if (f == 0)
                {
                    return flow;
                }
                flow += f;
            }
        }

        public void AddEdge(int from, int to, int cap)
        {
            if (!m_edges.ContainsKey(from))
            {
                m_edges.Add(from, new List<Edge>());
            }

            if (!m_edges.ContainsKey(to))
            {
                m_edges.Add(to, new List<Edge>());
            }

            m_edges[from].Add(new Edge()
            {
                To = to,
                Capacity = cap,
                Reverse = m_edges[to].Count,
            });
            m_edges[to].Add(new Edge()
            {
                To = from,
                Capacity = 0,
                Reverse = m_edges[from].Count - 1,
            });
        }

        private int Dfs(int v, int t, int f, bool[] used)
        {
            if (v == t)
            {
                return f;
            }

            used[v] = true;
            foreach (var edge in m_edges[v])
            {
                if (!used[edge.To] && edge.Capacity > 0)
                {
                    int d = Dfs(edge.To, t, Math.Min(f, edge.Capacity), used);
                    if (d > 0)
                    {
                        edge.Capacity -= d;
                        m_edges[edge.To][edge.Reverse].Capacity += d;
                        return d;
                    }
                }
            }

            return 0;
        }
    }

    class Red
    {
        public int x;
        public int y;
    }

    class Blue
    {
        public int x;
        public int y;
    }

    static class Program
    {
        static void Main(string[] args)
        {
            var i = new Parser(Console.OpenStandardInput());
            var o = new Printer(Console.OpenStandardOutput());
            var got = new Quest().Solve(i);
            o.WriteLine(got);
            o.Flush();
        }
    }
}
namespace AtCoder.ABC.IO
{
    #region IO

    using System;
    using System.IO;
    using System.Text;
    using System.Linq;
    using System.Collections.Generic;
    using System.Globalization;

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

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof;

        public bool IsEndOfStream
        {
            get { return isEof; }
        }

        public IEnumerable<Parser> Take(int n)
        {
            return Enumerable.Range(1, n).Select(_ => this);
        }

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

        public char Char()
        {
            byte b;
            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 = (char)read())
                if (b == 0) break;
                else if (b != '\r') sb.Append(b);
            return sb.ToString();
        }

        public long Long()
        {
            if (isEof) return long.MinValue;
            long ret = 0;
            byte b;
            var ng = false;
            do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b));
            if (b == 0) return long.MinValue;
            if (b == '-')
            {
                ng = true;
                b = read();
            }
            for (; ; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                ret = ret * 10 + b - '0';
            }
        }

        public int Integer()
        {
            return (isEof) ? int.MinValue : (int)Long();
        }

        public double Double()
        {
            var s = Scan();
            return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN;
        }

        static T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public char[] Char(int n)
        {
            return enumerate(n, Char);
        }

        public string[] Scan(int n)
        {
            return enumerate(n, Scan);
        }

        public double[] Double(int n)
        {
            return enumerate(n, Double);
        }

        public int[] Integer(int n)
        {
            return enumerate(n, Integer);
        }

        public long[] Long(int n)
        {
            return enumerate(n, Long);
        }
    }

    public class Printer : StreamWriter
    {
        public override IFormatProvider FormatProvider
        {
            get { return CultureInfo.InvariantCulture; }
        }

        public Printer(Stream stream)
            : base(stream, new UTF8Encoding(false, true))
        {
        }

        public Printer(Stream stream, Encoding encoding)
            : base(stream, encoding)
        {
        }

        public void Write<T>(string format, T[] source)
        {
            base.Write(format, source.OfType<object>().ToArray());
        }

        public void WriteLine<T>(string format, T[] source)
        {
            base.WriteLine(format, source.OfType<object>().ToArray());
        }
    }

    #endregion

}