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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

/**
 *
 * @author baito
 */
public class Main
{
    static StringBuilder sb = new StringBuilder();
    static FastScanner sc = new FastScanner(System.in);
    static int INF = 10000;
    static long MOD =1000000007;
    static long[] f;//factorial
    static int[] y4 = {0,1,0,-1};
    static int[] x4 = {1,0,-1,0};
    static int[] y8 = {0,1,0,-1,-1,1,1,-1};
    static int[] x8 = {1,0,-1,0,1,-1,1,-1};

    static int N;
    static int[] A;

    public static void main(String[] args)
    {
        N = sc.nextInt();
        A =new int[N+2];
        A[0] = 0;
        A[N+1]=0;
        long cou = 0;
        for (int i = 1; i < N+1; i++)
            A[i] = sc.nextInt();
        //longを忘れるなオーバーフローするぞ
        for (int i = 1; i < N+2; i++)
            cou+=Math.abs(A[i]-A[i-1]);
        //出力
        for (int i = 1; i < N+1; i++)
        {
            long ans = cou-abs(A[i]-A[i-1])-abs(A[i+1]-A[i]);
            ans += abs(A[i + 1] - A[i-1]);
            System.out.println(ans);
        }


    }
    //↓nCrをmod計算するために必要。　***factorial(N)を呼ぶ必要がある***
    static long comb(int n, int r)
    {
        long result = f[n];
        result = result * modInv(f[n - r]) % MOD;
        result = result * modInv(f[r]) % MOD;
        return result;
    }

    static long modInv(long n)
    {
        return modPow(n, MOD - 2);
    }

    static void factorial(int n)
    {
        f = new long[n + 1];
        f[0] = f[1] = 1;
        for (int i = 2; i <= n; i++)
        {
            f[i] = (f[i - 1] * i) % MOD;
        }
    }

    static long modPow(long x, long n)
    {
        long res = 1L;
        while (n > 0)
        {
            if ((n & 1) == 1)
            {
                res = res * x % MOD;
            }
            x = x * x % MOD;
            n >>= 1;
        }
        return res;
    }

    //↑nCrをmod計算するために必要

    static int gcd(int n, int r) { return r == 0 ? n : gcd(r, n%r); }
    static long gcd(long n, long r) { return r == 0 ? n : gcd(r, n%r); }

    static <T> void swap(T[] x, int i, int j) { T t = x[i]; x[i] = x[j]; x[j] = t; }
    static void swap(int[] x, int i, int j) { int t = x[i]; x[i] = x[j]; x[j] = t; }
    public static void reverse(int[] x)
    {
        int l = 0;
        int r = x.length - 1;
        while (l < r)
        {
            int temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }
    public static void reverse(int[] x,int s, int e)
    {
        int l = s;
        int r = e;
        while (l < r)
        {
            int temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }
    static int length(int a) {int cou = 0; while(a != 0){ a /= 10; cou++; } return cou;}
    static int length(long a) {int cou = 0; while(a != 0){ a /= 10; cou++; } return cou;}
    static int countC2(char[][] a, char c){
        int co = 0;
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                if(a[i][j] == c)
                    co++;
        return co;
    }
    static void fill(int[][] a, int v){
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                a[i][j] = v;
    }
    static int max(int a,int b, int c){
        return Math.max(a,Math.max(b,c));
    }
    static int abs(int a){
        return Math.abs(a);
    }

    static class FastScanner {

        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        public String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        /*public String nextChar(){
            return (char)next()[0];
        }*/
        public String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }

            return tokenizer.nextToken("\n");
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }
        public int [][] nextIntArray2(int h, int w){
            int[][] a = new int[h][w];
            for(int hi = 0 ; hi < h ; hi++){
                for(int wi = 0 ; wi < w ; wi++){
                    a[hi][wi] = nextInt();
                }
            }
            return a;
        }
        public Integer[] nextIntegerArray(int n) {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }
        public char[] nextCharArray(int n){
            char[] a = next().toCharArray();

            return a;
        }
        public char[][] nextCharArray2(int h , int w){
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++) {
                a[i] = next().toCharArray();
            }
            return a;
        }
        //スペースが入っている場合
        public char[][] nextCharArray2s(int h , int w){
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++) {
                a[i] = nextLine().replace(" ","").toCharArray();
            }
            return a;
        }
        public char[][] nextWrapCharArray2(int h , int w, char c){
            char[][] a = new char[h + 2][w + 2];
            //char c = '*';
            int i;
            for (i = 0; i < w + 2; i++)
                a[0][i] = c;
            for (i = 1; i < h + 1; i++) {
                a[i] = (c + next() + c).toCharArray();
            }
            for (i = 0; i < w + 2; i++)
                a[h + 1][i] = c;
            return a;
        }
        //スペースが入ってる時用
        public char[][] nextWrapCharArray2s(int h , int w ,char c){
            char[][] a = new char[h + 2][w + 2];
            //char c = '*';
            int i;
            for (i = 0; i < w + 2; i++)
                a[0][i] = c;
            for (i = 1; i < h + 1; i++) {
                a[i] = (c + nextLine().replace(" ","") + c).toCharArray();
            }
            for (i = 0; i < w + 2; i++)
                a[h + 1][i] = c;
            return a;
        }
        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }
        public long [][] nextLongArray2(int h, int w){
            long[][] a = new long[h][w];
            for(int hi = 0 ; hi < h ; hi++){
                for(int wi = 0 ; wi < h ; wi++){
                    a[h][w] = nextLong();
                }
            }
            return a;
        }
    }
}