#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class t, class u>
void chmax(t& first, u second) {
  if (first < second) first = second;
}
template <class t, class u>
void chmin(t& first, u second) {
  if (second < first) first = second;
}
template <class t>
using vc = vector<t>;
template <class t>
using vvc = vc<vc<t>>;
using pi = pair<ll, ll>;
using vi = vc<ll>;
template <class t, class u>
ostream& operator<<(ostream& os, const pair<t, u>& p) {
  return os << "{" << p.first << "," << p.second << "}";
}
template <class t>
ostream& operator<<(ostream& os, const vc<t>& v) {
  os << "{";
  for (auto e : v) os << e << ",";
  return os << "}";
}
using uint = unsigned;
using ull = unsigned long long;
template <class t, size_t n>
ostream& operator<<(ostream& os, const array<t, n>& first) {
  return os << vc<t>(first.begin(), first.end());
}
template <ll i, class T>
void print_tuple(ostream&, const T&) {}
template <ll i, class T, class H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ",";
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << "{";
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << "}";
}
template <class t>
void print(t x, ll suc = 1) {
  cout << x;
  if (suc == 1) cout << "\n";
  if (suc == 2) cout << " ";
}
ll read() {
  ll i;
  cin >> i;
  return i;
}
vi readvi(ll n, ll off = 0) {
  vi v(n);
  for (ll i = ll(0); i < ll(n); i++) v[i] = read() + off;
  return v;
}
pi readpi(ll off = 0) {
  ll first, second;
  cin >> first >> second;
  return pi(first + off, second + off);
}
template <class T>
void print(const vector<T>& v, ll suc = 1) {
  for (ll i = ll(0); i < ll(v.size()); i++)
    print(v[i], i == ll(v.size()) - 1 ? suc : 2);
}
string readString() {
  string s;
  cin >> s;
  return s;
}
template <class T>
T sq(const T& t) {
  return t * t;
}
void yes(bool ex = true) {
  cout << "Yes"
       << "\n";
  if (ex) exit(0);
}
void no(bool ex = true) {
  cout << "No"
       << "\n";
  if (ex) exit(0);
}
void possible(bool ex = true) {
  cout << "Possible"
       << "\n";
  if (ex) exit(0);
}
void impossible(bool ex = true) {
  cout << "Impossible"
       << "\n";
  if (ex) exit(0);
}
constexpr ll ten(ll n) { return n == 0 ? 1 : ten(n - 1) * 10; }
const ll infLL = LLONG_MAX / 3;
const ll inf = infLL;
ll topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
ll topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
ll botbit(signed first) { return first == 0 ? 32 : __builtin_ctz(first); }
ll botbit(ll first) { return first == 0 ? 64 : __builtin_ctzll(first); }
ll popcount(signed t) { return __builtin_popcount(t); }
ll popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(ll i) { return i && (i & -i) == i; }
ll mask(ll i) { return (ll(1) << i) - 1; }
bool inc(ll first, ll second, ll c) { return first <= second && second <= c; }
template <class t>
void mkuni(vc<t>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
ll rand_int(ll l, ll r) {
  static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
  return uniform_int_distribution<ll>(l, r)(gen);
}
template <class t>
void myshuffle(vc<t>& first) {
  for (ll i = ll(0); i < ll(ll(first.size())); i++)
    swap(first[i], first[rand_int(0, i)]);
}
template <class t>
ll lwb(const vc<t>& v, const t& first) {
  return lower_bound(v.begin(), v.end(), first) - v.begin();
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
  ll n;
  cin >> n;
  ll k = n / 2;
  vi x(k), y(n - k);
  for (ll i = ll(0); i < ll(k); i++) x[i] = i + 1;
  for (ll i = ll(0); i < ll(n - k); i++) y[i] = k + i + 1;
  vvc<ll> ans;
  if (n % 2) {
    for (ll i = ll(0); i < ll(k); i++)
      for (ll j = ll(i + 1); j < ll(k); j++)
        for (ll _ = ll(0); _ < ll(2); _++) {
          ans.push_back({x[i], x[j], y[i], y[j]});
        }
    for (ll i = ll(0); i < ll(k); i++)
      for (ll _ = ll(0); _ < ll(2); _++) ans.push_back({x[i], y[k], y[i]});
  } else {
    for (ll i = ll(0); i < ll(k); i++) {
      for (ll j = ll(i + 2); j < ll(i == 0 ? k - 1 : k); j++)
        for (ll _ = ll(0); _ < ll(2); _++) {
          ans.push_back({x[i], x[j], y[i], y[j]});
        }
      if (k >= 3) {
        if (i + 1 < k) {
          ll j = i + 1;
          ans.push_back({x[i], x[j], y[i], y[j]});
        }
        if (i == 0) {
          ll j = k - 1;
          ans.push_back({x[i], x[j], y[i], y[j]});
        }
      }
      {
        ans.push_back({x[i], x[(i + 1) % k], y[(i + 1) % k]});
        ans.push_back({x[(i + 1) % k], y[i], y[(i + 1) % k]});
      }
    }
  }
  print(ll(ans.size()));
  for (auto vs : ans) {
    print(ll(vs.size()), 2);
    print(vs);
  }
  vvc<ll> cnt(n, vi(n));
  for (auto vs : ans) {
    for (ll i = ll(0); i < ll(ll(vs.size())); i++) {
      ll p = vs[i] - 1, q = vs[(i + 1) % ll(vs.size())] - 1;
      cnt[p][q]++;
      cnt[q][p]++;
    }
  }
  void(0);
  for (ll i = ll(0); i < ll(n); i++)
    for (ll j = ll(0); j < ll(n); j++)
      if (i != j) {
        assert(cnt[i][j] == 2);
      }
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

In order to fly to the Moon Mister B just needs to solve the following problem.

There is a complete indirected graph with n vertices. You need to cover it with several simple cycles of length 3 and 4 so that each edge is in exactly 2 cycles.

We are sure that Mister B will solve the problem soon and will fly to the Moon. Will you?

Input

The only line contains single integer n (3 ≤ n ≤ 300).

Output

If there is no answer, print -1.

Otherwise, in the first line print k (1 ≤ k ≤ n2) — the number of cycles in your solution.

In each of the next k lines print description of one cycle in the following format: first print integer m (3 ≤ m ≤ 4) — the length of the cycle, then print m integers v1, v2, ..., vm (1 ≤ vi ≤ n) — the vertices in the cycle in the traverse order. Each edge should be in exactly two cycles.

Examples

Input

3


Output

2
3 1 2 3
3 1 2 3


Input

5


Output

6
3 5 4 2
3 3 1 5
4 4 5 2 3
4 4 3 2 1
3 4 2 1
3 3 1 5

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class t, class u>
void chmax(t& first, u second) {
  if (first < second) first = second;
}
template <class t, class u>
void chmin(t& first, u second) {
  if (second < first) first = second;
}
template <class t>
using vc = vector<t>;
template <class t>
using vvc = vc<vc<t>>;
using pi = pair<ll, ll>;
using vi = vc<ll>;
template <class t, class u>
ostream& operator<<(ostream& os, const pair<t, u>& p) {
  return os << "{" << p.first << "," << p.second << "}";
}
template <class t>
ostream& operator<<(ostream& os, const vc<t>& v) {
  os << "{";
  for (auto e : v) os << e << ",";
  return os << "}";
}
using uint = unsigned;
using ull = unsigned long long;
template <class t, size_t n>
ostream& operator<<(ostream& os, const array<t, n>& first) {
  return os << vc<t>(first.begin(), first.end());
}
template <ll i, class T>
void print_tuple(ostream&, const T&) {}
template <ll i, class T, class H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ",";
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << "{";
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << "}";
}
template <class t>
void print(t x, ll suc = 1) {
  cout << x;
  if (suc == 1) cout << "\n";
  if (suc == 2) cout << " ";
}
ll read() {
  ll i;
  cin >> i;
  return i;
}
vi readvi(ll n, ll off = 0) {
  vi v(n);
  for (ll i = ll(0); i < ll(n); i++) v[i] = read() + off;
  return v;
}
pi readpi(ll off = 0) {
  ll first, second;
  cin >> first >> second;
  return pi(first + off, second + off);
}
template <class T>
void print(const vector<T>& v, ll suc = 1) {
  for (ll i = ll(0); i < ll(v.size()); i++)
    print(v[i], i == ll(v.size()) - 1 ? suc : 2);
}
string readString() {
  string s;
  cin >> s;
  return s;
}
template <class T>
T sq(const T& t) {
  return t * t;
}
void yes(bool ex = true) {
  cout << "Yes"
       << "\n";
  if (ex) exit(0);
}
void no(bool ex = true) {
  cout << "No"
       << "\n";
  if (ex) exit(0);
}
void possible(bool ex = true) {
  cout << "Possible"
       << "\n";
  if (ex) exit(0);
}
void impossible(bool ex = true) {
  cout << "Impossible"
       << "\n";
  if (ex) exit(0);
}
constexpr ll ten(ll n) { return n == 0 ? 1 : ten(n - 1) * 10; }
const ll infLL = LLONG_MAX / 3;
const ll inf = infLL;
ll topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
ll topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
ll botbit(signed first) { return first == 0 ? 32 : __builtin_ctz(first); }
ll botbit(ll first) { return first == 0 ? 64 : __builtin_ctzll(first); }
ll popcount(signed t) { return __builtin_popcount(t); }
ll popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(ll i) { return i && (i & -i) == i; }
ll mask(ll i) { return (ll(1) << i) - 1; }
bool inc(ll first, ll second, ll c) { return first <= second && second <= c; }
template <class t>
void mkuni(vc<t>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
ll rand_int(ll l, ll r) {
  static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
  return uniform_int_distribution<ll>(l, r)(gen);
}
template <class t>
void myshuffle(vc<t>& first) {
  for (ll i = ll(0); i < ll(ll(first.size())); i++)
    swap(first[i], first[rand_int(0, i)]);
}
template <class t>
ll lwb(const vc<t>& v, const t& first) {
  return lower_bound(v.begin(), v.end(), first) - v.begin();
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
  ll n;
  cin >> n;
  ll k = n / 2;
  vi x(k), y(n - k);
  for (ll i = ll(0); i < ll(k); i++) x[i] = i + 1;
  for (ll i = ll(0); i < ll(n - k); i++) y[i] = k + i + 1;
  vvc<ll> ans;
  if (n % 2) {
    for (ll i = ll(0); i < ll(k); i++)
      for (ll j = ll(i + 1); j < ll(k); j++)
        for (ll _ = ll(0); _ < ll(2); _++) {
          ans.push_back({x[i], x[j], y[i], y[j]});
        }
    for (ll i = ll(0); i < ll(k); i++)
      for (ll _ = ll(0); _ < ll(2); _++) ans.push_back({x[i], y[k], y[i]});
  } else {
    for (ll i = ll(0); i < ll(k); i++) {
      for (ll j = ll(i + 2); j < ll(i == 0 ? k - 1 : k); j++)
        for (ll _ = ll(0); _ < ll(2); _++) {
          ans.push_back({x[i], x[j], y[i], y[j]});
        }
      if (k >= 3) {
        if (i + 1 < k) {
          ll j = i + 1;
          ans.push_back({x[i], x[j], y[i], y[j]});
        }
        if (i == 0) {
          ll j = k - 1;
          ans.push_back({x[i], x[j], y[i], y[j]});
        }
      }
      {
        ans.push_back({x[i], x[(i + 1) % k], y[(i + 1) % k]});
        ans.push_back({x[(i + 1) % k], y[i], y[(i + 1) % k]});
      }
    }
  }
  print(ll(ans.size()));
  for (auto vs : ans) {
    print(ll(vs.size()), 2);
    print(vs);
  }
  vvc<ll> cnt(n, vi(n));
  for (auto vs : ans) {
    for (ll i = ll(0); i < ll(ll(vs.size())); i++) {
      ll p = vs[i] - 1, q = vs[(i + 1) % ll(vs.size())] - 1;
      cnt[p][q]++;
      cnt[q][p]++;
    }
  }
  void(0);
  for (ll i = ll(0); i < ll(n); i++)
    for (ll j = ll(0); j < ll(n); j++)
      if (i != j) {
        assert(cnt[i][j] == 2);
      }
}

```