#include <bits/stdc++.h>
using namespace std;
using namespace chrono;

using ll = long long;
using ull = unsigned long long;

string to_string(const string &s) {
  return '"' + s + '"';
}

string to_string(bool b) {
  return b ? "true" : "false";
}

template <typename A, typename B>
string to_string(const pair<A, B> &p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename T>
string to_string(const T &v) {
  string s = "{";
  bool first = true;
  for (const auto &it : v) {
    if (!first)
      s += ", ";
    else
      first = false;
    s += to_string(it);
  }
  return s += "}";
}

void debug_out() {
  cerr << endl;
}

template <typename T, typename... Args>
void debug_out(const T &first, const Args&... rest) {
  cerr << to_string(first) << " ";
  debug_out(rest...);
}

#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

auto startTime = high_resolution_clock::now();
int get_time() {
  auto stopTime = chrono::high_resolution_clock::now();
  auto duration = duration_cast<milliseconds>(stopTime - startTime);
  return duration.count(); // in ms
}

const int DIM = 5e5 + 1;

int n;
int a[DIM];
pair<int, int> arb[4 * DIM];
void build(int st = 1, int dr = n, int nod = 1) {
  arb[nod] = {a[st], st};
  if (st == dr)
    return;

  int mij = (st + dr) / 2;
  build(st, mij, nod * 2);
  build(mij + 1, dr, nod * 2 + 1);

  arb[nod] = max(arb[nod * 2], arb[nod * 2 + 1]);
} 

pair<int,int> query(int x, int y, int st = 1, int dr = n, int nod = 1) {
  if (x <= st && dr <= y)
    return arb[nod];

  int mij = (st + dr) / 2;
  if (x <= mij && mij + 1 <= y)
    return max(query(x, y, st, mij, nod * 2), query(x, y, mij + 1, dr, nod * 2 + 1));

  if (x <= mij)
    return query(x, y, st, mij, nod * 2);

  return query(x, y, mij + 1, dr, nod * 2 + 1);
}

void solve() {
  cin >> n;
  for (int i = 1; i <= n; ++i)
    cin >> a[i];

  auto get_contribution = [&](int l, int r, int i, int x, int xl, int xr) -> ll {
    return 1LL * (r - l) * x - 1LL * (r - i) * xl - 1LL * (i - l) * xr;
  };

  build();

  std::function<ll(int, int)> solve = [&](int l, int r) -> ll {
    if (l + 1 >= r)
      return 0;

    auto res = query(l + 1, r - 1);
    int mx = res.first;
    int x = res.second;

    ll contrib = get_contribution(l, r, x, mx, a[l], a[r]);
    if (contrib > 0) {
      return contrib + solve(l, x) + solve(x, r);
    }

    return 0;
  };

  
  ll ans = solve(1, n) + 1LL * (n - 1) * (a[n] + a[1]);
  cout << ans << "\n";
}

int main() {
  cin.tie(NULL);
  ios_base::sync_with_stdio(false);

  int t = 1;
  cin >> t;
  while (t--)
    solve();

  return 0;
}