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

#define loop(i, a, b) for(int i = a; i <= b; i++)
#define loop_rev(i, a, b) for(int i = a; i >= b; i--)
#define all(x) x.begin(), x.end()
#define sz(x) int(x.size())
#define pb push_back

void solve();

inline int rint() {
  static char c; int res = 0;
  while(!isdigit(c = getchar_unlocked())) {}
  do { res = 10 * res + (c - '0'); }
  while(isdigit(c = getchar_unlocked()));
  return res;
}

inline void pint(int x, char sep = '\n') {
  static char buff[100];
  static int ptr = 0;
  do { buff[ptr++] = '0' + x % 10; x /= 10; } while(x);
  while(ptr) { putchar_unlocked(buff[--ptr]); }
  putchar_unlocked(sep);
}

signed main() {
  // cin.tie(0)->sync_with_stdio(0);
  int t = rint();
  while(t--) {
    solve();
  }
}

#define int _ll
using _ll = long long;

void solve() {
  int n = rint();

  vector<int> x(n + 1);
  int k = 0, max_x = 0;

  loop(i, 1, n) {
    x[i] = rint();
    if(x[i] > 0) {
      max_x = max(max_x, x[i]);
      ++k;
    }
  }

  int MAX_P, MAX_A;
  MAX_P = max(6LL, int(1.5 * ceil(sqrt(max_x))));
  MAX_A = int(ceil(sqrt(max_x)));

  loop(i, 1, n) {
    if(!x[i]) continue;
    int l = 0, r = x[i] + 100;
    while(l < r) {
      int mid = (l + r) / 2;
      if(mid * (mid - 1) * (mid - 2) / 6 >= x[i]) {
        r = mid;
      }
      else {
        l = mid + 1;
      }
    }
    MAX_A = max(MAX_A, l);
  }

  vector<int> ind_l;
  loop(i, 1, n) {
    if(x[i] || (i == 1) || (i == n)) ind_l.pb(i);
    if(sz(ind_l) > MAX_P / 2 + 5) break;
  }

  vector<int> ind_r;
  {
    loop_rev(i, n, 1) {
      if(i <= ind_l.back()) break;
      if(x[i]) ind_r.pb(i);
      if(sz(ind_r) > MAX_P / 2 + 5) break;
    }
    reverse(all(ind_r));
  }

  int pref_add = 0;
  if(sz(ind_r)) {
    loop(i, ind_l.back() + 1, ind_r[0] - 1) {
      pref_add += (x[i] > 0);
    }
  }

  auto fend = [&](int a, int lim, int s) {
    return a * (a - 1) * (a - 2) / 6 + a * (a - 1) / 2 * (s - a) >= lim;
  };


  {
    int l = 0, r = MAX_P;
    while(l < r) {
      int mid = (l + r) / 2;
      int s = k + mid;
      int pref = 0;
      vector<int> prep_ca(MAX_A + 1);
      loop(a, 1, MAX_A) {
        prep_ca[a] = (a * (a - 1) * (a - 2) / 6 + a * (a - 1) / 2 * (s - a));
      }
      // cerr << "---\n";
      int mini_p = 0, mini_p_new;
      auto calc = [&](int i) {
        mini_p_new = 1e9;
        loop(a, 0, min(MAX_A, mid)) {
          if(a > s) break;
          if(i == n) {
            int p = mid - a + (x[i] > 0);
            if(p >= 0 && p <= mid && p >= mini_p && prep_ca[a] >= x[i]) {
              mini_p_new = mid;
              break;
            }
            continue;
          }
          if(a == 0) {
            if(x[i] == 0) {
              mini_p_new = mini_p;
              break;
            }
            continue;
          }
          // given the a, solve for p - a quadratic equation
          int bb = (a * s - a * a);
          int aa = (-a);
          int cc = prep_ca[a] - x[i];
          int delta = bb * bb - 4 * aa * cc;
          if(delta >= 0) {
            double delta_sqrt = sqrt(delta);
            double p1ld = 2 * cc / (-bb - delta_sqrt);
            double p2ld = 2 * cc / (-bb + delta_sqrt);
            if(p1ld > p2ld) swap(p1ld, p2ld);
            int p1 = int(ceil(p1ld)) - pref;
            int p2 = int(floor(p2ld)) - pref;
            p1 = max(p1, 0LL);
            p2 = min(p2, mid);
            if(p1 <= p2) {
              if(p2 >= mini_p) {
                mini_p_new = min(mini_p_new, max(p1, mini_p) + (a - (x[i] > 0)));
              }
            }
          }
        }
        swap(mini_p_new, mini_p);
        pref += (x[i] > 0);
      };
      for(int i : ind_l) {
        calc(i);
      }
      pref += pref_add;
      for(int i : ind_r) {
        calc(i);
      }
      if(mini_p <= mid) {
        r = mid;
      }
      else {
        l = mid + 1;
      }
    }
    pint(k + l, '\n');
  }

}