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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define rep(i, s, N) for (ll i{s}; i < (N); i++)
#define rem(i, N, s) for (ll i{N}; i > (s); i--)
#define debug(x) cerr << #x << ": " << x << '\n'
#define debugv(v) cerr << #v << ": ";for(auto&& i : v) cerr << i << " "; cerr << '\n'
const int MOD = (int)1e9 + 7;
const long double pi = 3.141592653589793238462643383279L;
using namespace std;
using ll = long long;
using ld = long double;
using str = string;
using wstr = wstring;
const string rt = "\n", sp = " ";
const wstring wrt = L"\n", wsp = L" ";

/* GCD */
template <typename M, typename N>
constexpr common_type_t<M, N> gcd(M a, N b) { return b != 0 ? gcd(b, a % b) : a; }

/* LCM */
template <typename M, typename N>
constexpr common_type_t<M, N> lcm(M a, N b) { return a * b / gcd(a, b); }

/* UNIONFIND */
template <typename T>
struct UnionFind
{
  vector<T> par;
  UnionFind(T n) : par(n, -1) {}
  void init(T n) { par.assign(n, -1); }
  T root(T x)
  {
    if (par[x] < 0)
      return x;
    else
      return par[x] = root(par[x]);
  }
  bool issame(T x, T y) { return root(x) == root(y); }
  bool merge(T x, T y)
  {
    x = root(x);
    y = root(y);
    if (x == y)
      return false;
    if (par[x] > par[y])
      swap(x, y);
    par[x] += par[y];
    par[y] = x;
    return true;
  }
  int size(int x) { return -par[root(x)]; }
};

/* COMB */
auto comb(ll N){
  vector<vector<ll>> v(N+1,vector<ll>(N+1));
  for(int i = 0;i <v.size(); i++){
    v[i][0]=1;
    v[i][i]=1;
  }
  for(int k = 1;k <v.size();k++){
    for(int j = 1;j<k;j++){
      v[k][j]=(v[k-1][j-1]+v[k-1][j]);
    }
  }
  return v;
}
auto comb(ll N, ll n){
  vector<vector<ll>> v(max(N+1,n+1),vector<ll>(max(N+1,n+1)));
  for(int i = 0;i <v.size(); i++){
    v[i][0]=1;
    v[i][i]=1;
  }
  for(int k = 1;k <v.size();k++){
    for(int j = 1;j<k;j++){
      v[k][j]=(v[k-1][j-1]+v[k-1][j]);
    }
  }
  return v[N][n];
}

/* COMB % MOD */
template <typename T>
ll combpm(T N_, T C_)
{
  const int NUM_ = 400001;
  static ll fact[NUM_ + 1], factr[NUM_ + 1], inv[NUM_ + 1];
  if (fact[0] == 0)
  {
    inv[1] = fact[0] = factr[0] = 1;
    for (int i = 2; i <= NUM_; ++i)
      inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD;
    for (int i = 1; i <= NUM_; ++i)
      fact[i] = fact[i - 1] * i % MOD, factr[i] = factr[i - 1] * inv[i] % MOD;
  }
  if (C_ < 0 || C_ > N_)
    return 0;
  return factr[C_] * fact[N_] % MOD * factr[N_ - C_] % MOD;
}

/* MAKE VECTOR */
template <class T>
constexpr vector<T> mvec(size_t a) { return vector<T>(a); }
template <class T, class... Ts>
auto mvec(size_t a, Ts... ts) { return vector<decltype(mvec<T>(ts...))>(a, mvec<T>(ts...)); }

/* MAKE DEQUE */
template <class T>
constexpr deque<T> mdeq(size_t a) { return deque<T>(a); }
template <class T, class... Ts>
auto mdeq(size_t a, Ts... ts) { return deque<decltype(mdeq<T>(ts...))>(a, mdeq<T>(ts...)); }

/* TEST */
void test(ll n) { cout << "test" << n << endl; }

/* PRECISION */
void fixsp(ll n) { cout << fixed << setprecision(n); }
void defsp(ll n) { cout << defaultfloat << setprecision(n); }

/* WEIGHTENED UNIONFIND */
struct WUnionFind
{
  vector<int> par;
  vector<int> rank;
  WUnionFind(int n = 1) { init(n); }
  void init(int n = 1)
  {
    par.resize(n);
    rank.resize(n);
    for (int i = 0; i < n; ++i)
      par[i] = i, rank[i] = 0;
  }
  int root(int x)
  {
    if (par[x] == x)
    {
      return x;
    }
    else
    {
      int r = root(par[x]);
      return par[x] = r;
    }
  }
  bool issame(int x, int y) { return root(x) == root(y); }
  bool merge(int x, int y)
  {
    x = root(x);
    y = root(y);
    if (x == y)
      return false;
    if (rank[x] < rank[y])
      swap(x, y);
    if (rank[x] == rank[y])
      ++rank[x];
    par[y] = x;
    return true;
  }
};

/* DIVISOR */
deque<ll> divisor(ll n)
{
  deque<ll> ret;
  for (ll i = 1; i * i <= n; i++)
  {
    if (n % i == 0)
    {
      ret.push_back(i);
      if (i * i != n)
        ret.push_back(n / i);
    }
  }
  sort(begin(ret), end(ret));
  return (ret);
}

/* MODE */
template <typename T>
auto mode(T data)
{
  if (data.size() == 1)
    return *begin(data);
  sort(begin(data), end(data));
  typename decltype(data)::value_type mode{};
  size_t n{}, count{1};
  for (auto iter = adjacent_find(begin(data), end(data)), last = end(data), next = end(data); iter != last;)
  {
    next = upper_bound(iter, last, *iter);
    count = distance(iter, next);
    if (n < count)
      n = count, mode = *iter;
    iter = adjacent_find(next, last);
  }
  return mode;
}

/* MEDIAN */
template <typename T>
auto median(T data)
{
  sort(begin(data), end(data));
  size_t median_index = data.size() / 2;
  return (data.size() % 2 == 0 ? static_cast<double>(data[median_index] + data[median_index - 1]) / 2 : data[median_index]);
}

/* INT POW */
template <typename T>
T multi(T a, ll b)
{
  T ans{1};
  for (int i{}; i < b; i++)
    ans *= a;
  return ans;
}

/* INF */
template <typename T>
constexpr T inf() { return numeric_limits<T>::max(); } 

/* FASTER IO */
void fastio(ll a)
{
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  if(a) fixsp(a);
}

/* MIN COST FLOW */
template <typename flow_t, typename cost_t>
struct PrimalDual
{
  const cost_t INF;
  struct edge
  {
    int to;
    flow_t cap;
    cost_t cost;
    int rev;
    bool isrev;
  };
  vector<vector<edge>> graph;
  vector<cost_t> potential, min_cost;
  vector<int> prevv, preve;
  PrimalDual(int V) : graph(V), INF(numeric_limits<cost_t>::max()) {}
  void add_edge(int from, int to, flow_t cap, cost_t cost)
  {
    graph[from].emplace_back((edge){to, cap, cost, (int)graph[to].size(), false});
    graph[to].emplace_back((edge){from, 0, -cost, (int)graph[from].size() - 1, true});
  }
  cost_t min_cost_flow(int s, int t, flow_t f)
  {
    int V = (int)graph.size();
    cost_t ret = 0;
    using Pi = pair<cost_t, int>;
    priority_queue<Pi, vector<Pi>, greater<Pi>> que;
    potential.assign(V, 0);
    preve.assign(V, -1);
    prevv.assign(V, -1);
    while (f > 0)
    {
      min_cost.assign(V, INF);
      que.emplace(0, s);
      min_cost[s] = 0;
      while (!que.empty())
      {
        Pi p = que.top();
        que.pop();
        if (min_cost[p.second] < p.first)
          continue;
        for (int i = 0; i < graph[p.second].size(); i++)
        {
          edge &e = graph[p.second][i];
          cost_t nextCost = min_cost[p.second] + e.cost + potential[p.second] - potential[e.to];
          if (e.cap > 0 && min_cost[e.to] > nextCost)
          {
            min_cost[e.to] = nextCost;
            prevv[e.to] = p.second, preve[e.to] = i;
            que.emplace(min_cost[e.to], e.to);
          }
        }
      }
      if (min_cost[t] == INF)
        return -1;
      for (int v = 0; v < V; v++)
        potential[v] += min_cost[v];
      flow_t addflow = f;
      for (int v = t; v != s; v = prevv[v])
      {
        addflow = min(addflow, graph[prevv[v]][preve[v]].cap);
      }
      f -= addflow;
      ret += addflow * potential[t];
      for (int v = t; v != s; v = prevv[v])
      {
        edge &e = graph[prevv[v]][preve[v]];
        e.cap -= addflow;
        graph[v][e.rev].cap += addflow;
      }
    }
    return ret;
  }
  void output()
  {
    for (int i = 0; i < graph.size(); i++)
    {
      for (auto &e : graph[i])
      {
        if (e.isrev)
          continue;
        auto &rev_e = graph[e.to][e.rev];
        cout << i << "->" << e.to << " (flow: " << rev_e.cap << "/" << rev_e.cap + e.cap << ")" << endl;
      }
    }
  }
};

/* BELLMANFORD */

vector<long long> BellmanFord(int s, int V, vector<tuple<long long,long long,long long>> &G)
{
  vector<long long> d(V, inf<long long>());
  vector<bool> neg(V);
  d[s] = 0;
  for (int i = 0; i < V - 1; ++i)
  {
    for (auto &&e : G)
    {
      if (d[get<0>(e)] == inf<long long>())
        continue;
      d[get<1>(e)] = min(d[get<1>(e)], d[get<0>(e)] + get<2>(e));
    }
  }
  for (int i = 0; i < V; ++i)
  {
    for (auto &&e : G)
    {
      if (d[get<0>(e)] == inf<long long>())
        continue;
      if (d[get<1>(e)] > d[get<0>(e)] + get<2>(e))
      {
        d[get<1>(e)] = d[get<0>(e)] + get<2>(e);
        neg[get<1>(e)] = 1;
      }
      if (neg[get<0>(e)])
        neg[get<1>(e)] = 1;
    }
  }
  for (int i = 0; i < V; i++)
  {
    if (neg[i])
      d[i] = -inf<long long>();
  }
  return d;
}

/* DIJKSTRA */

vector<long long> Dijkstra(int s, int V, vector<tuple<long long,long long,long long>> &G){
  vector<vector<pair<long long,long long>>> uv(V);
  for(auto&& i : G) uv[get<0>(i)].emplace_back(get<1>(i), get<2>(i));
  vector<long long> d(V, inf<long long>()/2);
  vector<long long> prev(V, -1);
  d[s] = 0;
  priority_queue<pair<long long,long long>,vector<pair<long long,long long>>,greater<pair<long long,long long>>> Q;
  rep(i,0,V) Q.emplace(d[i], i);
  while(!Q.empty()){
    long long u = Q.top().second;
    Q.pop();
    for(auto&& v : uv[u]){
      long long alt = d[u] + v.second;
      if(d[v.first] > alt){
        d[v.first] = alt;
        if(d[v.first] > inf<long long>()/4) d[v.first] = inf<long long>()/2;
        else if(d[v.first] < -inf<long long>()/4) d[v.first] = -inf<long long>()/2;
        prev[v.first] = u;
        Q.emplace(alt, v.first);
      }
    }
  }
  for(auto&& i : d){
    if(abs(i)>inf<long long>()/4) (i*=2)++;
  }
  return d;
}

/* BFS */

vector<long long> BFS(long long s, long long V, vector<pair<long long,long long>> &G){
  queue<long long> Q;
  vector<vector<long long>> uv(V);
  for(auto&& i : G) uv[i.first].emplace_back(i.second);
  vector<long long> d(V,inf<long long>());
  d[s] = 0;
  Q.emplace(s);
  while(!Q.empty()){
    long long v = Q.front();
    Q.pop();
    for(auto&& i : uv[v]){
      if(d[i] == inf<long long>()){
        d[i] = d[v]+1;
        Q.emplace(i);
      }
    }
  }
  return d;
}

/* WARSHALLFLOYD */
vector<vector<long long>> WarshallFloyd(int V, vector<tuple<long long,long long,long long>> &G){
  vector<vector<long long>> d(V, vector<long long>(V, inf<long long>()));
  for(auto&& i : G){
    d[get<0>(i)][get<1>(i)] = get<2>(i);
  }
  rep(k,0,V) rep(i,0,V) rep(j,0,V){
    if(d[i][k] != inf<ll>() && d[k][j] != inf<ll>())
    d[i][j] = min(d[i][j], d[i][k] + d[k][j]);
  }
  rep(i,0,V){
    d[i][i] = 0;
  }
  return d;
}

/* NUITA.INC & KYOTO UNIVERSITY */

/* LAST EDITED ON 8.20.2019 */

/* CODE STARTS FROM HERE */

int main(){
  fastio(0);
  ll N;
  cin >> N;
  auto A = mdeq<ll>(N);
  deque<ll> L, R, l, r;
  rep(i,0,N) cin >> A[i];
  A.emplace_back(0);
  A.emplace_front(0);
  deque<ll> DP;
  DP.emplace_back(abs(A[0]));
  rep(i,0,N+1){
    DP.emplace_back(DP.back() + abs(A[i+1]-A[i]));
  }
  deque<ll> ANS;
  rep(i,0,N){
    ANS.emplace_back(DP[i] + DP[N+1] - DP[i+2] + abs(A[i+2] - A[i]));
  }
  for(auto&& i : ANS){
    cout << i << rt;
  }
}