#include <bits/stdc++.h>
template <class T>
inline T read() {
  T r = 0, f = 0;
  char c;
  while (!isdigit(c = getchar())) f |= (c == '-');
  while (isdigit(c)) r = (r << 1) + (r << 3) + (c ^ 48), c = getchar();
  return f ? -r : r;
}
inline char getc() {
  char c;
  while (!isalpha(c = getchar()))
    ;
  return c;
}
template <class T>
inline T abs(T a) {
  return a < 0 ? -a : a;
}
template <class T>
inline T min(T a, T b) {
  return a < b ? a : b;
}
template <class T>
inline T max(T a, T b) {
  return a > b ? a : b;
}
inline long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
inline long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
inline long long qpow(long long a, int b, int MOD = 998244353) {
  long long ans = 1;
  for (; b; b >>= 1) {
    if (b & 1) (ans *= a) %= MOD;
    (a *= a) %= MOD;
  }
  return ans;
}
struct Z {
  int x;
  inline int val() const { return x; }
  inline int inv() const { return qpow(x, 998244353 - 2); }
  Z(int x = 0) : x(x) {}
  Z operator-() const {
    return Z((998244353 - x >= 998244353 ? 998244353 - x - 998244353
                                         : 998244353 - x));
  }
  Z &operator+=(const Z &z) {
    x = (x + z.x >= 998244353 ? x + z.x - 998244353 : x + z.x);
    return *this;
  }
  Z &operator-=(const Z &z) {
    x = (x - z.x < 0 ? x - z.x + 998244353 : x - z.x);
    return *this;
  }
  Z &operator*=(const Z &z) {
    x = 1ll * x * z.x % 998244353;
    return *this;
  }
  Z &operator/=(const Z &z) {
    x = 1ll * x * z.inv() % 998244353;
    return *this;
  }
  Z operator+(const Z &z) const {
    return Z((x + z.x >= 998244353 ? x + z.x - 998244353 : x + z.x));
  }
  Z operator-(const Z &z) const {
    return Z((x - z.x < 0 ? x - z.x + 998244353 : x - z.x));
  }
  Z operator*(const Z &z) const { return Z(1ll * x * z.x % 998244353); }
  Z operator/(const Z &z) const { return Z(1ll * x * z.inv() % 998244353); }
};
template <int T, class Tt>
struct Hash {
  struct E {
    Tt v;
    int w, nxt;
    E() {}
    E(Tt v, int w, int nxt) : v(v), w(w), nxt(nxt) {}
  } e[T + 100];
  int s_e, head[T + 100];
  std::vector<int> d;
  inline void a_e(int u, Tt v, int w) {
    e[++s_e] = E(v, w, head[u]);
    head[u] = s_e;
  }
  inline int H(Tt x) { return (1ll * x * x + (x & T) + (x ^ T)) % T + 1; }
  inline bool find(Tt x) {
    int u = H(x);
    for (int i = head[u]; i; i = e[i].nxt)
      if (e[i].v == x) return true;
    return false;
  }
  int &operator[](const Tt x) {
    int u = H(x);
    for (int i = head[u]; i; i = e[i].nxt)
      if (e[i].v == x) return e[i].w;
    a_e(u, x, 0);
    d.push_back(x);
    return e[head[u]].w;
  }
  inline void clear() {
    s_e = 0;
    for (auto u : d) head[H(u)] = 0;
    d.clear();
  }
};
namespace Math {
int frac[1001001], invf[1001001], inv[1001001];
inline void init(int N) {
  frac[0] = 1;
  for (int i = 1; i <= N; i++) frac[i] = 1ll * frac[i - 1] * i % 998244353;
  invf[N] = qpow(frac[N], 998244353 - 2);
  for (int i = N; i >= 1; i--) {
    invf[i - 1] = 1ll * invf[i] * i % 998244353;
    inv[i] = 1ll * invf[i] * frac[i - 1] % 998244353;
  }
}
inline long long C(int n, int m) {
  if (n < m || m < 0) return 0;
  return 1ll * frac[n] * invf[m] % 998244353 * invf[n - m] % 998244353;
}
}  // namespace Math
using namespace Math;
template <int T>
struct Polyn {
  int n, a[T];
  Polyn(int _n = 0) {
    n = _n;
    for (int i = 0; i < n; i++) a[i] = 0;
  }
  int &operator[](const int x) { return a[x]; }
  inline Polyn R() {
    Polyn b(n);
    for (int i = 0; i * 2 < n; i++) b[i] = a[n - 1 - i];
    return b;
  }
  inline Polyn Der() {
    Polyn b(n - 1);
    for (int i = 1; i < n; i++) b[i - 1] = 1ll * a[i] * i % 998244353;
    return b;
  }
  inline Polyn Int() {
    Polyn b(n + 1);
    for (int i = 1; i <= n; i++) b[i] = 1ll * a[i - 1] * inv[i] % 998244353;
    return b;
  }
  inline Polyn Inv() {
    Polyn b(n);
    b[0] = qpow(a[0], 998244353 - 2);
    long long inv = b[0];
    for (int i = 1; i < n; i++) {
      long long res = 0;
      for (int j = 0; j < i; j++) (res += 1ll * b[j] * a[i - j]) %= 998244353;
      b[i] = (998244353 - res) * inv % 998244353;
    }
    return b;
  }
  Polyn operator-() {
    Polyn b(*this);
    for (int i = 0; i < n; i++) b[i] = (998244353 - b[i]) % 998244353;
    return b;
  }
  Polyn operator+(int x) {
    Polyn b(*this);
    (b[0] += x) %= 998244353;
    return b;
  }
  Polyn operator-(int x) {
    Polyn b(*this);
    (b[0] += 998244353 - x) %= 998244353;
    return b;
  }
  Polyn operator*(int x) {
    Polyn b(*this);
    for (int i = 0; i < n; i++) b[i] = 1ll * b[i] * x % 998244353;
    return b;
  }
  Polyn operator+(Polyn b) {
    Polyn c = b;
    for (int i = 0; i < n; i++) (c[i] += a[i]) %= 998244353;
    return c;
  }
  Polyn operator-(Polyn b) {
    Polyn c = (*this);
    for (int i = 0; i < n; i++) (c[i] += 998244353 - b[i]) %= 998244353;
    return c;
  }
  Polyn operator*(Polyn b) {
    Polyn c(n + b.n - 1);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < b.n; j++)
        (c[i + j] += 1ll * a[i] * b[j] % 998244353) %= 998244353;
    return c;
  }
  Polyn operator/(Polyn b) { return (*this) * b.Inv(); }
  Polyn operator%(Polyn b) {
    Polyn r = (*this);
    for (int i = n - 1; i >= b.n - 1; i--) {
      int inv = r[i] * qpow(b[b.n - 1], 998244353 - 2);
      for (int j = i; j >= i - b.n + 1; j--)
        (r[j] += 998244353 - 1ll * b[j - i + b.n - 1] * inv % 998244353) %=
            998244353;
    }
    r.n = min(n, b.n - 1);
    return r;
  }
  inline int Y(int x) {
    int Sum = 0;
    for (int i = n - 1; ~i; i--) Sum = (1ll * Sum * x + a[i]) % 998244353;
    return Sum;
  }
};
template <int T>
struct Mat {
  int n, m, a[T + 3][T + 3];
  inline void init(int _n = 0, int _m = 0, bool o = 1) {
    n = _n, m = _m;
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) a[i][j] = i ^ j ? 0 : o;
  }
  Mat operator+(const Mat &b) const {
    Mat c(*this);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) (c.a[i][j] += b.a[i][j]) %= 998244353;
    return c;
  }
  Mat operator-(const Mat &b) const {
    Mat c(*this);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++)
        (c.a[i][j] += 998244353 - b.a[i][j]) %= 998244353;
    return c;
  }
  Mat operator*(const Mat &b) const {
    Mat c;
    c.init(n, b.m);
    for (int i = 0; i < n; i++)
      for (int k = 0; k < m; k++)
        for (int j = 0; j < b.m; j++)
          (c.a[i][j] += 1ll * a[i][k] * b.a[k][j] % 998244353) %= 998244353;
    return c;
  }
  Mat &operator+=(const Mat &b) {
    (*this) = (*this) + b;
    return *this;
  }
  Mat &operator-=(const Mat &b) {
    (*this) = (*this) - b;
    return *this;
  }
  Mat &operator*=(const Mat &b) {
    (*this) = (*this) * b;
    return *this;
  }
  bool operator==(const Mat &b) const {
    if (n != b.n || m != b.m) return false;
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++)
        if (a[i][j] != b.a[i][j]) return false;
    return true;
  }
  bool operator!=(const Mat &b) const { return !((*this) == b); }
};
int n, h[202202], d[202202], add[202202];
inline bool check(int mid) {
  for (int i = 1; i <= n; i++) d[i] = h[i], add[i] = 0;
  for (int i = n; i >= 3; i--) {
    if (d[i] < mid - add[i]) return false;
    int D = (d[i] - max(mid - add[i], 0)) / 3;
    add[i - 1] += D, add[i - 2] += 2 * D;
  }
  return add[1] + d[1] >= mid && add[2] + d[2] >= mid;
}
inline void work() {
  n = read<int>();
  for (int i = 1; i <= n; i++) h[i] = read<int>();
  int l = 1, r = 1e9 + 1;
  while (l + 1 < r) {
    int mid = (l + r) >> 1;
    if (check(mid))
      l = mid;
    else
      r = mid;
  }
  printf("%d\n", l);
}
int main() {
  int t = read<int>();
  while (t--) work();
  return 0;
}

### Prompt

Generate a CPP solution to the following problem:

There are n heaps of stone. The i-th heap has h_i stones. You want to change the number of stones in the heap by performing the following process once: 

  * You go through the heaps from the 3-rd heap to the n-th heap, in this order. 
  * Let i be the number of the current heap. 
  * You can choose a number d (0 ≤ 3 ⋅ d ≤ h_i), move d stones from the i-th heap to the (i - 1)-th heap, and 2 ⋅ d stones from the i-th heap to the (i - 2)-th heap. 
  * So after that h_i is decreased by 3 ⋅ d, h_{i - 1} is increased by d, and h_{i - 2} is increased by 2 ⋅ d. 
  * You can choose different or same d for different operations. Some heaps may become empty, but they still count as heaps. 



What is the maximum number of stones in the smallest heap after the process?

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 2⋅ 10^5). Description of the test cases follows.

The first line of each test case contains a single integer n (3 ≤ n ≤ 2 ⋅ 10^5).

The second lines of each test case contains n integers h_1, h_2, h_3, …, h_n (1 ≤ h_i ≤ 10^9).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, print the maximum number of stones that the smallest heap can contain.

Example

Input


4
4
1 2 10 100
4
100 100 100 1
5
5 1 1 1 8
6
1 2 3 4 5 6


Output


7
1
1
3

Note

In the first test case, the initial heap sizes are [1, 2, 10, 100]. We can move the stones as follows. 

  * move 3 stones and 6 from the 3-rd heap to the 2-nd and 1 heap respectively. The heap sizes will be [7, 5, 1, 100]; 
  * move 6 stones and 12 stones from the last heap to the 3-rd and 2-nd heap respectively. The heap sizes will be [7, 17, 7, 82]. 



In the second test case, the last heap is 1, and we can not increase its size.

In the third test case, it is better not to move any stones.

In the last test case, the final achievable configuration of the heaps can be [3, 5, 3, 4, 3, 3].

### Response

```cpp
#include <bits/stdc++.h>
template <class T>
inline T read() {
  T r = 0, f = 0;
  char c;
  while (!isdigit(c = getchar())) f |= (c == '-');
  while (isdigit(c)) r = (r << 1) + (r << 3) + (c ^ 48), c = getchar();
  return f ? -r : r;
}
inline char getc() {
  char c;
  while (!isalpha(c = getchar()))
    ;
  return c;
}
template <class T>
inline T abs(T a) {
  return a < 0 ? -a : a;
}
template <class T>
inline T min(T a, T b) {
  return a < b ? a : b;
}
template <class T>
inline T max(T a, T b) {
  return a > b ? a : b;
}
inline long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
inline long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
inline long long qpow(long long a, int b, int MOD = 998244353) {
  long long ans = 1;
  for (; b; b >>= 1) {
    if (b & 1) (ans *= a) %= MOD;
    (a *= a) %= MOD;
  }
  return ans;
}
struct Z {
  int x;
  inline int val() const { return x; }
  inline int inv() const { return qpow(x, 998244353 - 2); }
  Z(int x = 0) : x(x) {}
  Z operator-() const {
    return Z((998244353 - x >= 998244353 ? 998244353 - x - 998244353
                                         : 998244353 - x));
  }
  Z &operator+=(const Z &z) {
    x = (x + z.x >= 998244353 ? x + z.x - 998244353 : x + z.x);
    return *this;
  }
  Z &operator-=(const Z &z) {
    x = (x - z.x < 0 ? x - z.x + 998244353 : x - z.x);
    return *this;
  }
  Z &operator*=(const Z &z) {
    x = 1ll * x * z.x % 998244353;
    return *this;
  }
  Z &operator/=(const Z &z) {
    x = 1ll * x * z.inv() % 998244353;
    return *this;
  }
  Z operator+(const Z &z) const {
    return Z((x + z.x >= 998244353 ? x + z.x - 998244353 : x + z.x));
  }
  Z operator-(const Z &z) const {
    return Z((x - z.x < 0 ? x - z.x + 998244353 : x - z.x));
  }
  Z operator*(const Z &z) const { return Z(1ll * x * z.x % 998244353); }
  Z operator/(const Z &z) const { return Z(1ll * x * z.inv() % 998244353); }
};
template <int T, class Tt>
struct Hash {
  struct E {
    Tt v;
    int w, nxt;
    E() {}
    E(Tt v, int w, int nxt) : v(v), w(w), nxt(nxt) {}
  } e[T + 100];
  int s_e, head[T + 100];
  std::vector<int> d;
  inline void a_e(int u, Tt v, int w) {
    e[++s_e] = E(v, w, head[u]);
    head[u] = s_e;
  }
  inline int H(Tt x) { return (1ll * x * x + (x & T) + (x ^ T)) % T + 1; }
  inline bool find(Tt x) {
    int u = H(x);
    for (int i = head[u]; i; i = e[i].nxt)
      if (e[i].v == x) return true;
    return false;
  }
  int &operator[](const Tt x) {
    int u = H(x);
    for (int i = head[u]; i; i = e[i].nxt)
      if (e[i].v == x) return e[i].w;
    a_e(u, x, 0);
    d.push_back(x);
    return e[head[u]].w;
  }
  inline void clear() {
    s_e = 0;
    for (auto u : d) head[H(u)] = 0;
    d.clear();
  }
};
namespace Math {
int frac[1001001], invf[1001001], inv[1001001];
inline void init(int N) {
  frac[0] = 1;
  for (int i = 1; i <= N; i++) frac[i] = 1ll * frac[i - 1] * i % 998244353;
  invf[N] = qpow(frac[N], 998244353 - 2);
  for (int i = N; i >= 1; i--) {
    invf[i - 1] = 1ll * invf[i] * i % 998244353;
    inv[i] = 1ll * invf[i] * frac[i - 1] % 998244353;
  }
}
inline long long C(int n, int m) {
  if (n < m || m < 0) return 0;
  return 1ll * frac[n] * invf[m] % 998244353 * invf[n - m] % 998244353;
}
}  // namespace Math
using namespace Math;
template <int T>
struct Polyn {
  int n, a[T];
  Polyn(int _n = 0) {
    n = _n;
    for (int i = 0; i < n; i++) a[i] = 0;
  }
  int &operator[](const int x) { return a[x]; }
  inline Polyn R() {
    Polyn b(n);
    for (int i = 0; i * 2 < n; i++) b[i] = a[n - 1 - i];
    return b;
  }
  inline Polyn Der() {
    Polyn b(n - 1);
    for (int i = 1; i < n; i++) b[i - 1] = 1ll * a[i] * i % 998244353;
    return b;
  }
  inline Polyn Int() {
    Polyn b(n + 1);
    for (int i = 1; i <= n; i++) b[i] = 1ll * a[i - 1] * inv[i] % 998244353;
    return b;
  }
  inline Polyn Inv() {
    Polyn b(n);
    b[0] = qpow(a[0], 998244353 - 2);
    long long inv = b[0];
    for (int i = 1; i < n; i++) {
      long long res = 0;
      for (int j = 0; j < i; j++) (res += 1ll * b[j] * a[i - j]) %= 998244353;
      b[i] = (998244353 - res) * inv % 998244353;
    }
    return b;
  }
  Polyn operator-() {
    Polyn b(*this);
    for (int i = 0; i < n; i++) b[i] = (998244353 - b[i]) % 998244353;
    return b;
  }
  Polyn operator+(int x) {
    Polyn b(*this);
    (b[0] += x) %= 998244353;
    return b;
  }
  Polyn operator-(int x) {
    Polyn b(*this);
    (b[0] += 998244353 - x) %= 998244353;
    return b;
  }
  Polyn operator*(int x) {
    Polyn b(*this);
    for (int i = 0; i < n; i++) b[i] = 1ll * b[i] * x % 998244353;
    return b;
  }
  Polyn operator+(Polyn b) {
    Polyn c = b;
    for (int i = 0; i < n; i++) (c[i] += a[i]) %= 998244353;
    return c;
  }
  Polyn operator-(Polyn b) {
    Polyn c = (*this);
    for (int i = 0; i < n; i++) (c[i] += 998244353 - b[i]) %= 998244353;
    return c;
  }
  Polyn operator*(Polyn b) {
    Polyn c(n + b.n - 1);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < b.n; j++)
        (c[i + j] += 1ll * a[i] * b[j] % 998244353) %= 998244353;
    return c;
  }
  Polyn operator/(Polyn b) { return (*this) * b.Inv(); }
  Polyn operator%(Polyn b) {
    Polyn r = (*this);
    for (int i = n - 1; i >= b.n - 1; i--) {
      int inv = r[i] * qpow(b[b.n - 1], 998244353 - 2);
      for (int j = i; j >= i - b.n + 1; j--)
        (r[j] += 998244353 - 1ll * b[j - i + b.n - 1] * inv % 998244353) %=
            998244353;
    }
    r.n = min(n, b.n - 1);
    return r;
  }
  inline int Y(int x) {
    int Sum = 0;
    for (int i = n - 1; ~i; i--) Sum = (1ll * Sum * x + a[i]) % 998244353;
    return Sum;
  }
};
template <int T>
struct Mat {
  int n, m, a[T + 3][T + 3];
  inline void init(int _n = 0, int _m = 0, bool o = 1) {
    n = _n, m = _m;
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) a[i][j] = i ^ j ? 0 : o;
  }
  Mat operator+(const Mat &b) const {
    Mat c(*this);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) (c.a[i][j] += b.a[i][j]) %= 998244353;
    return c;
  }
  Mat operator-(const Mat &b) const {
    Mat c(*this);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++)
        (c.a[i][j] += 998244353 - b.a[i][j]) %= 998244353;
    return c;
  }
  Mat operator*(const Mat &b) const {
    Mat c;
    c.init(n, b.m);
    for (int i = 0; i < n; i++)
      for (int k = 0; k < m; k++)
        for (int j = 0; j < b.m; j++)
          (c.a[i][j] += 1ll * a[i][k] * b.a[k][j] % 998244353) %= 998244353;
    return c;
  }
  Mat &operator+=(const Mat &b) {
    (*this) = (*this) + b;
    return *this;
  }
  Mat &operator-=(const Mat &b) {
    (*this) = (*this) - b;
    return *this;
  }
  Mat &operator*=(const Mat &b) {
    (*this) = (*this) * b;
    return *this;
  }
  bool operator==(const Mat &b) const {
    if (n != b.n || m != b.m) return false;
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++)
        if (a[i][j] != b.a[i][j]) return false;
    return true;
  }
  bool operator!=(const Mat &b) const { return !((*this) == b); }
};
int n, h[202202], d[202202], add[202202];
inline bool check(int mid) {
  for (int i = 1; i <= n; i++) d[i] = h[i], add[i] = 0;
  for (int i = n; i >= 3; i--) {
    if (d[i] < mid - add[i]) return false;
    int D = (d[i] - max(mid - add[i], 0)) / 3;
    add[i - 1] += D, add[i - 2] += 2 * D;
  }
  return add[1] + d[1] >= mid && add[2] + d[2] >= mid;
}
inline void work() {
  n = read<int>();
  for (int i = 1; i <= n; i++) h[i] = read<int>();
  int l = 1, r = 1e9 + 1;
  while (l + 1 < r) {
    int mid = (l + r) >> 1;
    if (check(mid))
      l = mid;
    else
      r = mid;
  }
  printf("%d\n", l);
}
int main() {
  int t = read<int>();
  while (t--) work();
  return 0;
}

```