(source: https://dmoj.ca/problem/ciw26p2)

For her sixteenth birthday, Beryl received a lovely gift from her grandmother: an $$$N \times M$$$ grid of numbers. As per family tradition, she must now perform a sequence of $$$Q$$$ operations on the grid. Each operation is one of the following:

• Transpose the grid; i.e., swap its rows and columns so that the number in row $$$i$$$, column $$$j$$$ ends up in row $$$j$$$, column $$$i$$$. If the grid had $$$n$$$ rows and $$$m$$$ columns before this operation, it now has $$$m$$$ rows and $$$n$$$ columns.
• Given an integer $$$k$$$ that divides $$$NM$$$, reshape the grid so that it has $$$k$$$ rows and $$$NM/k$$$ columns. The numbers in the grid are unchanged, and they stay in the same order when read row by row.

What does the grid look like after performing the sequence of operations? $$$NM \le 5 \times 10^5$$$; $$$Q \le 5 \times 10^5$$$.

NT = int(input())
 
for T in range(NT):
	n = int(input())
	answer = [0, 0, 0, 0]
	first_card = 1
	for it in range(1, 20000):
		who = 0 if it % 4 == 1 or it % 4 == 0 else 1
		cnt = it
		if n < cnt:
			cnt = n
		cnt_white = (cnt + first_card % 2) // 2
		cnt_black = cnt - cnt_white
		answer[who * 2 + 0] += cnt_white
		answer[who * 2 + 1] += cnt_black
		first_card += cnt
		n -= cnt
		if n == 0:
			break
	assert(n == 0)
	print(*answer)
 

#include <bits/stdc++.h>

using namespace std;

const int inf = 1000000000;

int main() {
  int tt;
  cin >> tt;
  while (tt--) {
    int n, w, h;
    cin >> n >> w >> h;
    vector<int> a(n);
    for (int i = 0; i < n; i++) {
      cin >> a[i];
    }
    vector<int> b(n);
    for (int i = 0; i < n; i++) {
      cin >> b[i];
    }
    int minshift = -inf;
    int maxshift = inf;
    for (int i = 0; i < n; i++) {
      minshift = max(minshift, (b[i] + h) - (a[i] + w));
      maxshift = min(maxshift, (b[i] - h) - (a[i] - w));
    }
    if (minshift <= maxshift) {
      cout << "YES" << '\n';
    } else {
      cout << "NO" << '\n';
    }
  }
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

int main() {
  int tt;
  cin >> tt;
  while (tt--) {
    int n;
    cin >> n;
    vector<int> a(n);
    for (int i = 0; i < n; i++) {
      cin >> a[i];
    }
    sort(a.begin(), a.end());
    vector<int> b(n);
    b[0] = 1;
    for (int i = 1; i < n; i++) {
      b[i] = min(b[i - 1] + 1, a[i]);
    }
    long long ans = 0;
    for (int i = 0; i < n; i++) {
      ans += a[i] - b[i];
    }
    cout << ans << '\n';
  }
  return 0;
}

private fun IntArray.countOf(value: Int) = count { it == value }

private fun solve() {
    val s = "win"
    fun IntArray.bad() = (0 until 3).singleOrNull { c -> count { it == c } > 1 }
    val data = List(readInt()) { readLn().map { s.indexOf(it) }.toIntArray() }
    val ans = mutableListOf<String>()
    fun exchange(c1: Int, c2: Int, i1: Int, i2: Int) {
        ans.add("$$${i1+1} $$${s[c1]} $$${i2+1} $$${s[c2]}")
        val index1 = data[i1].indexOf(c1)
        val index2 = data[i2].indexOf(c2)
        data[i1][index1] = c2
        data[i2][index2] = c1
    }
    val todo = List(3) { List(3) { mutableListOf<Int> () } }
    for (i in data.indices) {
        val bad = data[i].bad() ?: continue
        for (j in 0 until 3) {
            if (data[i].countOf(j) == 0) {
                todo[bad][j].add(i)
            }
        }
    }

    for (i in 0 until 3) {
        for (j in 0 until 3) {
            if (i != j) {
                while (todo[i][j].isNotEmpty() && todo[j][i].isNotEmpty()) {
                    exchange(i, j, todo[i][j].removeLast(), todo[j][i].removeLast())
                }
            }
        }
    }
    while (todo[0][1].isNotEmpty() && todo[1][2].isNotEmpty() && todo[2][0].isNotEmpty()) {
        val a = todo[0][1].removeLast()
        val b = todo[1][2].removeLast()
        val c = todo[2][0].removeLast()
        exchange(0, 1, a, b)
        exchange(0, 2, b, c)
    }
    while (todo[1][0].isNotEmpty() && todo[2][1].isNotEmpty() && todo[0][2].isNotEmpty()) {
        val a = todo[1][0].removeLast()
        val b = todo[2][1].removeLast()
        val c = todo[0][2].removeLast()
        exchange(1, 0, a, c)
        exchange(2, 1, b, c)
    }
    println(ans.size)
    println(ans.joinToString("\n"))
}

fun main() {
    repeat(readInt()) {
        solve()
    }
}

private fun readLn() = readLine()!!
private fun readInt() = readLn().toInt()

#include <bits/stdc++.h>

using namespace std;

int main() {
  int tt;
  cin >> tt;
  while (tt--) {
    int n;
    cin >> n;
    vector<int> a(n);
    for (int i = 0; i < n; i++) {
      cin >> a[i];
    }
    vector<int> mn(2 * n - 1);
    vector<int> add(2 * n - 1, 0);
    vector<int> pos(2 * n - 1);
    auto Pull = [&](int x, int z) {
      mn[x] = min(mn[x + 1], mn[z]) + add[x];
      pos[x] = (mn[x + 1] <= mn[z] ? pos[x + 1] : pos[z]);
    };
    function<void(int, int, int, int, int, int)> Modify = [&](int x, int l, int r, int ll, int rr, int v) {
      if (ll <= l && r <= rr) {
        mn[x] += v;
        add[x] += v;
        return;
      }
      int y = (l + r) >> 1;
      int z = x + 2 * (y - l + 1);
      if (ll <= y) {
        Modify(x + 1, l, y, ll, rr, v);
      }
      if (rr > y) {
        Modify(z, y + 1, r, ll, rr, v);
      }
      Pull(x, z);
    };
    function<void(int, int, int)> Build = [&](int x, int l, int r) {
      if (l == r) {
        mn[x] = l;
        pos[x] = l;
        return;
      }
      int y = (l + r) >> 1;
      int z = x + 2 * (y - l + 1);
      Build(x + 1, l, y);
      Build(z, y + 1, r);
      Pull(x, z);
    };
    Build(0, 1, n);
    long long s = 0;
    long long m = 0;
    for (int i = 0; i < n; i++) {
      s += a[i];
      m += 1;
      Modify(0, 1, n, a[i], n, -1);
      if (mn[0] < 0) {
        s -= pos[0];
        m -= 1;
        Modify(0, 1, n, pos[0], n, +1);
      }
      cout << s - m * (m + 1) / 2 << " \n"[i == n - 1];
    }
  }
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a; swap(a, m);
    u -= t * v; swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }

  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }

  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const { return static_cast<U>(value); }
  constexpr static Type mod() { return T::value; }

  Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
  Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }

  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
    return *this;
  }

 private:
  Type value;
};

template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }

constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);

Mint C(int n, int k) {
  if (k < 0 || k > n) {
    return 0;
  }
  while ((int) fact.size() < n + 1) {
    fact.push_back(fact.back() * (int) fact.size());
    inv_fact.push_back(1 / fact.back());
  }
  return fact[n] * inv_fact[k] * inv_fact[n - k];
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  C(1 << n, 0);
  vector<Mint> dp(1 << n);
  dp[0] = (1 << n) * fact[1 << (n - 1)];
  for (int rd = n - 2; rd >= 0; rd--) {
    vector<Mint> new_dp(1 << n);
    Mint sum = 0;
    for (int i = 0; i < (1 << n); i++) {
      new_dp[i] = sum * C((1 << n) - 1 - i - (1 << rd), (1 << rd) - 1) * fact[1 << rd];
      sum += dp[i];
    }
    swap(dp, new_dp);
  }
  Mint sum = 0;
  for (int i = 0; i < (1 << n); i++) {
    cout << sum() << '\n';
    sum += dp[i];
  }
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }

  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }

  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const { return static_cast<U>(value); }
  constexpr static Type mod() { return T::value; }

  Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
  template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }

  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);

 private:
  Type value;
};

template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }

constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  string s;
  cin >> s;
  int len = (int) s.size();
  vector<Mint> ans(3);
  for (int use = 1; use < (1 << 4); use++) {
    int pw = 1 << 8;
    int init = 0;
    for (int i = 0; i < 4; i++) {
      init += i << (2 * i);
    }
    vector<vector<int>> go_state(pw, vector<int>(2));
    vector<vector<int>> go_diff(pw, vector<int>(2));
    for (int state = 0; state < pw; state++) {
      for (int put = 0; put < 2; put++) {
        int new_diff = 0;
        int new_state = 0;
        for (int i = 0; i < 4; i++) {
          int to = (state >> (2 * i)) & 3;
          if (put == 0) {
            if (to & 1) {
              if (use & (1 << i)) {
                new_diff += 1;
              }
              to = 0;
            } else {
              to |= 1;
            }
          } else {
            if (to & 2) {
              if (use & (1 << i)) {
                new_diff -= 1;
              }
              to = 0;
            } else {
              to |= 2;
            }
          }
          new_state += to << (2 * i);
        }
        go_state[state][put] = new_state;
        go_diff[state][put] = new_diff;
      }
    }
    int limit = (len + 1) / 2 * 2 * __builtin_popcount(use);
    vector<vector<Mint>> dp(2 * limit + 1, vector<Mint>(pw));
    dp[limit][init] = 1;
    for (char c : s) {
      vector<vector<Mint>> new_dp(2 * limit + 1, vector<Mint>(pw));
      for (int sum = 0; sum < (int) dp.size(); sum++) {
        for (int state = 0; state < pw; state++) {
          if (dp[sum][state] == 0) {
            continue;
          }
          for (int put = 0; put < 2; put++) {
            if ((put == 0 && c == 'b') || (put == 1 && c == 'a')) {
              continue;
            }
            int new_sum = sum + go_diff[state][put];
            int new_state = go_state[state][put];
            new_dp[new_sum][new_state] += dp[sum][state];
          }
        }
      }
      swap(dp, new_dp);
    }
    for (int sum = 0; sum < (int) dp.size(); sum++) {
      for (int state = 0; state < pw; state++) {
        if (dp[sum][state] == 0) {
          continue;
        }
        vector<int> to(4);
        for (int i = 0; i < 4; i++) {
          to[i] = (state >> (2 * i)) & 3;
        }
        vector<int> seq(1, 0);
        while (true) {
          int nxt = to[seq.back()];
          bool done = false;
          for (int i = 0; i < (int) seq.size(); i++) {
            if (seq[i] == nxt) {
              done = true;
              seq.erase(seq.begin(), seq.begin() + i);
              break;
            }
          }
          if (done) {
            break;
          }
          seq.push_back(nxt);
        }
        int real_use = 0;
        for (int x : seq) {
          real_use |= (1 << x);
        }
        if (use == real_use) {
          ans[sum > limit ? 0 : (sum < limit ? 2 : 1)] += dp[sum][state];
        }
      }
    }
  }
  for (int i = 0; i < 3; i++) {
    cout << ans[i]() << '\n';
  }
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a; swap(a, m);
    u -= t * v; swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }

  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }

  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const { return static_cast<U>(value); }
  constexpr static Type mod() { return T::value; }

  Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
  Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }

  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
    return *this;
  }

 private:
  Type value;
};

template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }

constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);

Mint C(int n, int k) {
  if (k < 0 || k > n) {
    return 0;
  }
  while ((int) fact.size() < n + 1) {
    fact.push_back(fact.back() * (int) fact.size());
    inv_fact.push_back(1 / fact.back());
  }
  return fact[n] * inv_fact[k] * inv_fact[n - k];
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  Mint ans = 1;
  for (int p = 1; p <= k; p++) {
    for (int q = 0; q <= max(0, k - 1 - p); q++) {
      if (2 * (k - p - q) + 1 <= n - p) {
        ans += (q == 0 ? 1 : C((k - 1 - p) - (q - 1), q));
      }
    }
  }
  for (int q = 1; q <= k - 1; q++) {
    int pos = 2 * (k - q) + 2;
    int shifts = max(1, pos - n);
    int left = k - shifts;
    ans += C(left - (q - 1), q);
  }
  cout << ans() << '\n';
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a; swap(a, m);
    u -= t * v; swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }

  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }

  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const { return static_cast<U>(value); }
  constexpr static Type mod() { return T::value; }

  Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
  Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }

  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
    return *this;
  }

 private:
  Type value;
};

template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }

constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);

Mint C(int n, int k) {
  if (k < 0 || k > n) {
    return 0;
  }
  while ((int) fact.size() < n + 1) {
    fact.push_back(fact.back() * (int) fact.size());
    inv_fact.push_back(1 / fact.back());
  }
  return fact[n] * inv_fact[k] * inv_fact[n - k];
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  Mint ans = 1;
  for (int q = 0; q <= k - 1; q++) {
    int bound = k - q - max(1, 2 * (k - q) - n + 1);
    ans += C(bound + 1, q + 1);
  }
  for (int q = 1; q <= k - 1; q++) {
    int pos = 2 * (k - q) + 2;
    int shifts = max(1, pos - n);
    int left = k - shifts;
    ans += C(left - (q - 1), q);
  }
  cout << ans() << '\n';
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

int main() {
  int tt;
  cin >> tt;
  while (tt--) {
    int w, d, h;
    cin >> w >> d >> h;
    int a, b;
    cin >> a >> b;
    int f, g;
    cin >> f >> g;
    int ans = b + abs(a - f) + g;
    ans = min(ans, a + abs(b - g) + f);
    ans = min(ans, (d - b) + abs(a - f) + (d - g));
    ans = min(ans, (w - a) + abs(b - g) + (w - f));
    cout << ans + h << '\n';
  }
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

int main() {
  int tt;
  cin >> tt;
  while (tt--) {
    int n;
    cin >> n;
    vector<int> cnt(n + 1);
    for (int i = 0; i < n; i++) {
      int a;
      cin >> a;
      cnt[a] += 1;
    }
    int ans = 0;
    int sum = 0;
    for (int k = 0; k <= n; k++) {
      if (cnt[k] == 0 && sum == k) {
        ans += 1;
      }
      sum += cnt[k];
    }
    cout << ans << '\n';
  }
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

int main() {
  int tt;
  cin >> tt;
  while (tt--) {
    int n;
    cin >> n;
    vector<int> a(n);
    for (int i = 0; i < n; i++) {
      cin >> a[i];
    }
    sort(a.begin(), a.end());
    int ans = 0;
    for (int k = 0; k <= n; k++) {
      if (k == 0 || a[k - 1] < k) {
        if (k == n || a[k] > k) {
          ans += 1;
        }
      }
    }
    cout << ans << '\n';
  }
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

int main() {
  int tt;
  cin >> tt;
  while (tt--) {
    int n;
    cin >> n;
    string s;
    cin >> s;
    vector<vector<int>> at(26);
    for (int i = 0; i < n; i++) {
      at[(int) (s[i] - 'a')].push_back(i);
    }
    vector<int> order(26);
    iota(order.begin(), order.end(), 0);
    sort(order.begin(), order.end(), [&](int i, int j) {
      return at[i].size() > at[j].size();
    });
    string res = "";
    int best = -1;
    for (int cnt = 1; cnt <= 26; cnt++) {
      if (n % cnt == 0) {
        int cur = 0;
        for (int i = 0; i < cnt; i++) {
          cur += min(n / cnt, (int) at[order[i]].size());
        }
        if (cur > best) {
          best = cur;
          res = string(n, ' ');
          vector<char> extra;
          for (int it = 0; it < cnt; it++) {
            int i = order[it];
            for (int j = 0; j < n / cnt; j++) {
              if (j < (int) at[i].size()) {
                res[at[i][j]] = (char) ('a' + i);
              } else {
                extra.push_back((char) ('a' + i));
              }
            }
          }
          for (char& c : res) {
            if (c == ' ') {
              c = extra.back();
              extra.pop_back();
            }
          }
        }
      }
    }
    cout << n - best << '\n';
    cout << res << '\n';
  }
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

int main() {
  int tt;
  cin >> tt;
  while (tt--) {
    int n;
    cin >> n;
    vector<int> a(n);
    for (int i = 0; i < n; i++) {
      cin >> a[i];
    }
    int ans = 1;
    auto Test = [&](long long x) {
      int cnt = 0;
      for (int v : a) {
        long long u = llround(sqrtl(v + x));
        if (u * u == v + x) {
          cnt += 1;
        }
      }
      ans = max(ans, cnt);
    };
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        int diff = a[j] - a[i];
        for (int k = 1; k * k <= diff; k++) {
          if (diff % k == 0) {
            long long q = k + diff / k;
            if (q % 2 == 0) {
              q /= 2;
              if (q * q >= a[j]) {
                Test(q * q - a[j]);
              }
            }
          }
        }
      }
    }
    cout << ans << '\n';
  }
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int tt;
  cin >> tt;
  while (tt--) {
    int n;
    cin >> n;
    vector<int> r1(n), c1(n), r2(n), c2(n);
    for (int i = 0; i < n; i++) {
      cin >> r1[i] >> c1[i] >> r2[i] >> c2[i];
      assert(1 <= r1[i] && r1[i] <= r2[i] && r2[i] <= 2 && c1[i] <= c2[i]);
      --c1[i];
    }
    vector<int> order(n);
    iota(order.begin(), order.end(), 0);
    sort(order.begin(), order.end(), [&](int i, int j) {
      return c1[i] < c1[j];
    });
    set<pair<int, int>> s;
    int ans = 0;
    int p1 = -1;
    int p2 = -1;
    for (int i : order) {
      if (r1[i] == 1 && r2[i] == 2) {
        if (p1 >= c2[i]) {
          r1[i] = 2;
        }
        if (p2 >= c2[i]) {
          r2[i] = 1;
        }
        if (r1[i] > r2[i]) {
          continue;
        }
      }
      if (r1[i] == 1 && r2[i] == 2) {
        while (!s.empty()) {
          auto it = prev(s.end());
          if (it->first >= c1[i]) {
            c2[it->second] = c1[i];
            s.erase(it);
          } else {
            break;
          }
        }
        ans += (c2[i] - max(c1[i], p1)) + (c2[i] - max(c1[i], p2));
        p1 = p2 = c2[i];
        s.emplace(c2[i], i);
        continue;
      }
      assert(r1[i] == r2[i]);
      if (r1[i] == 1) {
        c1[i] = max(c1[i], p1);
        p1 = max(p1, c2[i]);
      } else {
        c1[i] = max(c1[i], p2);
        p2 = max(p2, c2[i]);
      }
      if (c1[i] < c2[i]) {
        ans += c2[i] - c1[i];
        s.emplace(c2[i], i);
      }
    }
    cout << ans << '\n';
    for (int i = 0; i < n; i++) {
      ++c1[i];
      if (r1[i] <= r2[i] && c1[i] <= c2[i]) {
        cout << r1[i] << " " << c1[i] << " " << r2[i] << " " << c2[i] << '\n';
      } else {
        cout << "0 0 0 0" << '\n';
      }
    }
  }
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a; swap(a, m);
    u -= t * v; swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }

  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }

  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const { return static_cast<U>(value); }
  constexpr static Type mod() { return T::value; }

  Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
  Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
  template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
  template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
  Modular operator-() const { return Modular(-value); }

  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
    return *this;
  }

  Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }

  template <typename V, typename U>
  friend V& operator>>(V& stream, Modular<U>& number);

 private:
  Type value;
};

template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }

template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }

template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }

template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
  return stream << number();
}

template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, long long>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  Mint p;
  cin >> n >> p;
  p /= 10000;
  vector<vector<Mint>> C(n + 1, vector<Mint>(n + 1));
  for (int i = 0; i <= n; i++) {
    C[i][0] = 1;
    for (int j = 1; j <= i; j++) {
      C[i][j] = C[i - 1][j] + C[i - 1][j - 1];
    }
  }
  vector<vector<Mint>> dp(n + 1, vector<Mint>(n + 1));
  vector<vector<Mint>> aux(n + 1, vector<Mint>(n + 1));
  for (int b = 0; b <= n; b++) {
    dp[0][b] = aux[0][b] = 1;
  }
  for (int i = 1; i <= n; i++) {
    for (int b = 0; b <= n - i; b++) {
      for (int y = 0; y <= i - 1; y++) {
        dp[i][b] += C[i - 1][y] * aux[i - 1 - y][b] * (dp[y][b + 1] * p + (b == 0 ? 0 : dp[y][b - 1] * (1 - p)));
      }
      for (int j = 0; j <= i; j++) {
        aux[i][b] += dp[j][b] * dp[i - j][b] * C[i][j];
      }
    }
  }
  auto ans = dp[n][0];
  for (int i = 1; i <= 2 * n; i += 2) {
    ans /= i;
  }
  cout << ans << '\n';
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int tt;
  cin >> tt;
  while (tt--) {
    int n;
    cin >> n;
    vector<int> p(n);
    for (int i = 1; i < n; i++) {
      cin >> p[i];
      --p[i];
    }
    for (int i = 2; i <= n; i++) {
      if (i == 4 && p[1] == 0 && p[2] == 1 && p[3] == 1) {
        cout << 2 << '\n';
      } else {
        cout << i % 2 << '\n';
      }
    }
    vector<vector<int>> g(n);
    for (int i = 1; i < n; i++) {
      g[p[i]].push_back(i);
    }
    string res = "";
    auto Solve = [&](int nn) {
      vector<vector<vector<bool>>> good(nn);
      vector<vector<vector<vector<int>>>> prevs(nn);
      vector<int> sz(nn);
      vector<int> L(nn);
      vector<int> R(nn);
      function<void(int)> Dfs = [&](int v) {
        sz[v] += 1;
        for (int u : g[v]) {
          Dfs(u);
          sz[v] += sz[u];
        }
        L[v] = sz[v] / 2;
        R[v] = L[v] + 1;
        good[v].assign(2, vector<bool>(R[v] - L[v] + 1, false));
        prevs[v].assign(2, vector<vector<int>>(R[v] - L[v] + 1));
        auto Set = [&](int c, int k, vector<int> pr) {
          if (k >= L[v] && k <= R[v]) {
            good[v][c][k - L[v]] = true;
            prevs[v][c][k - L[v]] = pr;
          }
        };
        if (g[v].size() == 0) {
          Set(0, 1, {});
        }
        if (g[v].size() == 1) {
          int u = g[v][0];
          for (int cu = 0; cu < 2; cu++) {
            for (int ku = L[u]; ku <= R[u]; ku++) {
              if (good[u][cu][ku - L[u]]) {
                Set(1, 1 + (sz[u] - ku), {cu, ku, 1});
                if (cu == 1) {
                  Set(0, 1 + ku, {cu, ku, 0});
                }
              }
            }
          }
        }
        if (g[v].size() == 2) {
          int u = g[v][0];
          int w = g[v][1];
          for (int cu = 0; cu < 2; cu++) {
            for (int ku = L[u]; ku <= R[u]; ku++) {
              if (good[u][cu][ku - L[u]]) {
                for (int cw = 0; cw < 2; cw++) {
                  for (int kw = L[w]; kw <= R[w]; kw++) {
                    if (good[w][cw][kw - L[w]]) {
                      Set(1, 1 + (sz[u] - ku) + (sz[w] - kw), {cu, ku, 1, cw, kw, 1});
                      if (cu == 1) {
                        Set(1, 1 + ku + (sz[w] - kw), {cu, ku, 0, cw, kw, 1});
                      }
                      if (cw == 1) {
                        Set(1, 1 + (sz[u] - ku) + kw, {cu, ku, 1, cw, kw, 0});
                      }
                      if (cu == 1 && cw == 1) {
                        Set(0, 1 + ku + kw, {cu, ku, 0, cw, kw, 0});
                      }
                    }
                  }
                }
              }
            }
          }
        }
      };
      Dfs(0);
      int best = nn + 1;
      int best_k = -1;
      for (int k = L[0]; k <= R[0]; k++) {
        if (good[0][1][k - L[0]]) {
          int val = abs(k - (nn - k));
          if (val < best) {
            best = val;
            best_k = k;
          }
        }
      }
      assert(best <= nn);
      res = string(nn, '.');
      function<void(int, int, int)> Restore = [&](int v, int c, int k) {
        int ptr = 0;
        for (int u : g[v]) {
          res[u] = (prevs[v][c][k - L[v]][ptr + 2] == 0 ? res[v] : (char) ('w' ^ 'b' ^ res[v]));
          Restore(u, prevs[v][c][k - L[v]][ptr], prevs[v][c][k - L[v]][ptr + 1]);
          ptr += 3;
        }
      };
      res[0] = 'w';
      Restore(0, 1, best_k);
      return best;
    };
    Solve(n);
    cout << res << '\n';
  }
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a; swap(a, m);
    u -= t * v; swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }

  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }

  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const { return static_cast<U>(value); }
  constexpr static Type mod() { return T::value; }

  Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
  Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
  template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
  template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
  Modular operator-() const { return Modular(-value); }

  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
    return *this;
  }

  Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }

  template <typename V, typename U>
  friend V& operator>>(V& stream, Modular<U>& number);

 private:
  Type value;
};

template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }

template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }

template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }

template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}

template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
  return stream << number();
}

template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, long long>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

int main() {
  int tt;
  cin >> tt;
  while (tt--) {
    int h, w, k;
    cin >> h >> w >> k;
    vector<Mint> fib(h * w + 1);
    fib[0] = 1;
    fib[1] = 2;
    for (int i = 2; i <= h * w; i++) {
      fib[i] = fib[i - 1] + fib[i - 2];
    }
    vector<pair<int, int>> p(k);
    for (int i = 0; i < k; i++) {
      cin >> p[i].first >> p[i].second;
      --p[i].first; --p[i].second;
    }
    long long Q = 0;
    Mint ans = 0;
    for (int ww = 1; ww <= w; ww++) {
      for (int hh = 1; hh <= h; hh++) {
        for (int top = 0; top < 2; top++) {
          for (int bottom = 0; bottom < 2; bottom++) {
            for (int left = 0; left < 2; left++) {
              for (int right = 0; right < 2; right++) {
                int sign = ((top + bottom + left + right) % 2 == 0 ? 1 : -1);
                int rh = max(0, hh - top - bottom);
                int rw = max(0, ww - left - right);
                Q += rh * rw + (h - hh) * (w - ww);
                ans += sign * power(Mint(2), rh * rw);
                vector<vector<int>> g(hh * ww);
                vector<bool> must(hh * ww, false);
                bool any = false;
                for (int i = 0; i <= h - hh; i++) {
                  for (int j = 0; j <= w - ww; j++) {
                    vector<pair<int, int>> here;
                    for (auto& c : p) {
                      if (c.first >= i + top && c.first < i + hh - bottom && c.second >= j + left && c.second < j + ww - right) {
                        here.emplace_back(c.first - i - top, c.second - j - left);
                      }
                    }
                    if (here.size() == 0) {
                      any = true;
                    }
                    if (here.size() == 1) {
                      int x = here[0].first * rw + here[0].second;
                      must[x] = true;
                    }
                    if (here.size() == 2) {
                      int x = here[0].first * rw + here[0].second;
                      int y = here[1].first * rw + here[1].second;
                      g[x].push_back(y);
                      g[y].push_back(x);
                    }
                  }
                }
                if (!any) {
                  Mint ways = 1;
                  vector<bool> was(rh * rw, false);
                  for (int i = 0; i < rh * rw; i++) {
                    if (!was[i] && g[i].empty()) {
                      was[i] = true;
                      if (!must[i]) {
                        ways *= 2;
                      }
                    }
                  }
                  for (int i = 0; i < rh * rw; i++) {
                    if (!was[i] && g[i].size() == 1) {
                      vector<bool> seq;
                      int x = i;
                      while (true) {
                        was[x] = true;
                        seq.push_back(must[x]);
                        int to = -1;
                        for (int y : g[x]) {
                          if (!was[y]) {
                            to = y;
                            break;
                          }
                        }
                        if (to == -1) {
                          break;
                        }
                        x = to;
                      }
                      int sz = (int) seq.size();
                      int beg = 0;
                      while (beg < sz) {
                        if (seq[beg]) {
                          beg += 1;
                          continue;
                        }
                        int end = beg;
                        while (end + 1 < sz && !seq[end + 1]) {
                          end += 1;
                        }
                        int len = end - beg + 1;
                        ways *= fib[len];
                        beg = end + 1;
                      }
                    }
                  }
                  assert(was == vector<bool>(rh * rw, true));
                  ans -= sign * ways;
                }
              }
            }
          }
        }
      }
    }
    cout << ans << '\n';
  }
  return 0;
}

#include <bits/stdc++.h>

using namespace std;

template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a; swap(a, m);
    u -= t * v; swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }

  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }

  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const { return static_cast<U>(value); }
  constexpr static Type mod() { return T::value; }

  Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
  Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
  template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
  template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
  Modular operator-() const { return Modular(-value); }

  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
    return *this;
  }

  Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }

  template <typename V, typename U>
  friend V& operator>>(V& stream, Modular<U>& number);

 private:
  Type value;
};

template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }

template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }

template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }

template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}

template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
  return stream << number();
}

template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, long long>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

class dsu {
 public:
  vector<int> p;
  vector<int> sz;
  int n;

  dsu(int _n) : n(_n) {
    p.resize(n);
    iota(p.begin(), p.end(), 0);
    sz.assign(n, 1);
  }

  inline int get(int x) {
    return (x == p[x] ? x : (p[x] = get(p[x])));
  }

  inline bool unite(int x, int y) {
    x = get(x);
    y = get(y);
    if (x != y) {
      p[x] = y;
      sz[y] += sz[x];
      return true;
    }
    return false;
  }
};

int main() {
  int tt;
  cin >> tt;
  while (tt--) {
    int h, w, k;
    cin >> h >> w >> k;
    vector<Mint> fib(h * w + 1);
    fib[0] = 1;
    fib[1] = 2;
    for (int i = 2; i <= h * w; i++) {
      fib[i] = fib[i - 1] + fib[i - 2];
    }
    vector<pair<int, int>> p(k);
    for (int i = 0; i < k; i++) {
      cin >> p[i].first >> p[i].second;
      --p[i].first; --p[i].second;
    }
    Mint ans = 0;
    for (int ww = 1; ww <= w; ww++) {
      for (int top = 0; top < 2; top++) {
        for (int left = 0; left < 2; left++) {
          for (int right = 0; right < 2; right++) {
            if (ww == 1 && left + right > 0) {
              continue;
            }
            int sign = ((top + left + right) % 2 == 0 ? 1 : -1);
            dsu d(h * ww);
            vector<vector<int>> g(h * ww);
            vector<bool> must(h * ww);
            bool done = false;
            Mint prod = power(Mint(2), (h - top) * (ww - left - right));
            for (int i = 0; i < h; i++) {
              for (int j = 0; j <= w - ww; j++) {
                vector<pair<int, int>> here;
                for (auto& c : p) {
                  if (c.first >= i + top && c.second >= j + left && c.second < j + ww - right) {
                    here.emplace_back(c.first - i, c.second - j);
                  }
                }
                if (here.size() == 0) {
                  ans += sign * prod;
                  done = true;
                  break;
                }
                if (here.size() == 1) {
                  int x = here[0].first * ww + here[0].second;
                  if (!must[x]) {
                    must[x] = true;
                    int px = d.get(x);
                    prod /= fib[d.sz[px]];
                    d.sz[px] -= 1;
                    int sub = 0;
                    for (int y : g[x]) {
                      if (!must[y]) {
                        sub += 1;
                      }
                    }
                    ans += sign * prod * fib[d.sz[px] - sub];
                    prod *= fib[d.sz[px]];
                  }
                }
                if (here.size() == 2) {
                  int x = here[0].first * ww + here[0].second;
                  int y = here[1].first * ww + here[1].second;
                  int px = d.get(x);
                  int py = d.get(y);
                  assert(px != py);
                  prod /= fib[d.sz[px]];
                  prod /= fib[d.sz[py]];
                  if (!must[x] && !must[y]) {
                    int subx = 1;
                    for (int t : g[x]) {
                      if (!must[t]) {
                        subx += 1;
                      }
                    }
                    int suby = 1;
                    for (int t : g[y]) {
                      if (!must[t]) {
                        suby += 1;
                      }
                    }
                    ans += sign * prod * fib[d.sz[px] - subx] * fib[d.sz[py] - suby];
                    g[x].push_back(y);
                    g[y].push_back(x);
                  }
                  d.unite(px, py);
                  prod *= fib[d.sz[py]];
                }
              }
              if (done) {
                break;
              }
              for (int j = left; j < ww - right; j++) {
                int x = (h - 1 - i) * ww + j;
                if (must[x]) {
                  done = true;
                  break;
                }
                int px = d.get(x);
                prod /= fib[d.sz[px]];
                d.sz[px] -= 1;
                prod *= fib[d.sz[px]];
                for (int y : g[x]) {
                  if (!must[y]) {
                    must[y] = true;
                    int py = d.get(y);
                    prod /= fib[d.sz[py]];
                    d.sz[py] -= 1;
                    prod *= fib[d.sz[py]];
                  }
                }
              }
              if (done) {
                break;
              }
            }
          }
        }
      }
    }
    cout << ans << '\n';
  }
  return 0;
}