Timus-Ship-Routes-1172

#include     <bits/stdc++.h>
#ifndef      CONVICTION
#define      debug(x...)
#endif
#define IOS  ios_base::sync_with_stdio(false); cin.tie (nullptr)
#define PREC cout.precision (10); cout << fixed
#define F    first
#define S    second
#define Int  long long
#define ff   long double
using namespace std;
//Don’t practice until you get it right. Practice until you can’t get it wrong
struct bigint {
   static const int base = 1000000000;
   static const int base_digits = 9;

   vector<int> a;
   int sign;
   /*<arpa>*/
   int size(){
      if(a.empty())return 0;
      int ans=(a.size()-1)*base_digits;
      int ca=a.back();
      while(ca)
         ans++,ca/=10;
      return ans;
   }
   bigint operator ^(const bigint &v){
      bigint ans=1,a=*this,b=v;
      while(!b.isZero()){
         if(b%2)
            ans*=a;
         a*=a,b/=2;
      }
      return ans;
   }
   string to_string(){
      stringstream ss;
      ss << *this;
      string s;
      ss >> s;
      return s;
   }
   int sumof(){
      string s = to_string();
      int ans = 0;
      for(auto c : s)  ans += c - '0';
      return ans;
   }
   /*</arpa>*/
   bigint() :
   sign(1) {
   }

   bigint(long long v) {
      *this = v;
   }

   bigint(const string &s) {
      read(s);
   }

   void operator=(const bigint &v) {
      sign = v.sign;
      a = v.a;
   }

   void operator=(long long v) {
      sign = 1;
      a.clear();
      if (v < 0)
         sign = -1, v = -v;
      for (; v > 0; v = v / base)
         a.push_back(v % base);
   }

   bigint operator+(const bigint &v) const {
      if (sign == v.sign) {
         bigint res = v;

         for (int i = 0, carry = 0; i < (int) max(a.size(), v.a.size()) || carry; ++i) {
            if (i == (int) res.a.size())
               res.a.push_back(0);
            res.a[i] += carry + (i < (int) a.size() ? a[i] : 0);
            carry = res.a[i] >= base;
            if (carry)
               res.a[i] -= base;
         }
         return res;
      }
      return *this - (-v);
   }

   bigint operator-(const bigint &v) const {
      if (sign == v.sign) {
         if (abs() >= v.abs()) {
            bigint res = *this;
            for (int i = 0, carry = 0; i < (int) v.a.size() || carry; ++i) {
               res.a[i] -= carry + (i < (int) v.a.size() ? v.a[i] : 0);
               carry = res.a[i] < 0;
               if (carry)
                  res.a[i] += base;
            }
            res.trim();
            return res;
         }
         return -(v - *this);
      }
      return *this + (-v);
   }

   void operator*=(int v) {
      if (v < 0)
         sign = -sign, v = -v;
      for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {
         if (i == (int) a.size())
            a.push_back(0);
         long long cur = a[i] * (long long) v + carry;
         carry = (int) (cur / base);
         a[i] = (int) (cur % base);
         //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));
      }
      trim();
   }

   bigint operator*(int v) const {
      bigint res = *this;
      res *= v;
      return res;
   }

   void operator*=(long long v) {
      if (v < 0)
         sign = -sign, v = -v;
      for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {
         if (i == (int) a.size())
            a.push_back(0);
         long long cur = a[i] * (long long) v + carry;
         carry = (int) (cur / base);
         a[i] = (int) (cur % base);
         //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));
      }
      trim();
   }

   bigint operator*(long long v) const {
      bigint res = *this;
      res *= v;
      return res;
   }

   friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
      int norm = base / (b1.a.back() + 1);
      bigint a = a1.abs() * norm;
      bigint b = b1.abs() * norm;
      bigint q, r;
      q.a.resize(a.a.size());

      for (int i = a.a.size() - 1; i >= 0; i--) {
         r *= base;
         r += a.a[i];
         int s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
         int s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
         int d = ((long long) base * s1 + s2) / b.a.back();
         r -= b * d;
         while (r < 0)
            r += b, --d;
         q.a[i] = d;
      }

      q.sign = a1.sign * b1.sign;
      r.sign = a1.sign;
      q.trim();
      r.trim();
      return make_pair(q, r / norm);
   }

   bigint operator/(const bigint &v) const {
      return divmod(*this, v).first;
   }

   bigint operator%(const bigint &v) const {
      return divmod(*this, v).second;
   }

   void operator/=(int v) {
      if (v < 0)
         sign = -sign, v = -v;
      for (int i = (int) a.size() - 1, rem = 0; i >= 0; --i) {
         long long cur = a[i] + rem * (long long) base;
         a[i] = (int) (cur / v);
         rem = (int) (cur % v);
      }
      trim();
   }

   bigint operator/(int v) const {
      bigint res = *this;
      res /= v;
      return res;
   }

   int operator%(int v) const {
      if (v < 0)
         v = -v;
      int m = 0;
      for (int i = a.size() - 1; i >= 0; --i)
         m = (a[i] + m * (long long) base) % v;
      return m * sign;
   }

   void operator+=(const bigint &v) {
      *this = *this + v;
   }
   void operator-=(const bigint &v) {
      *this = *this - v;
   }
   void operator*=(const bigint &v) {
      *this = *this * v;
   }
   void operator/=(const bigint &v) {
      *this = *this / v;
   }

   bool operator<(const bigint &v) const {
      if (sign != v.sign)
         return sign < v.sign;
      if (a.size() != v.a.size())
         return a.size() * sign < v.a.size() * v.sign;
      for (int i = a.size() - 1; i >= 0; i--)
         if (a[i] != v.a[i])
            return a[i] * sign < v.a[i] * sign;
         return false;
   }

   bool operator>(const bigint &v) const {
      return v < *this;
   }
   bool operator<=(const bigint &v) const {
      return !(v < *this);
   }
   bool operator>=(const bigint &v) const {
      return !(*this < v);
   }
   bool operator==(const bigint &v) const {
      return !(*this < v) && !(v < *this);
   }
   bool operator!=(const bigint &v) const {
      return *this < v || v < *this;
   }

   void trim() {
      while (!a.empty() && !a.back())
         a.pop_back();
      if (a.empty())
         sign = 1;
   }

   bool isZero() const {
      return a.empty() || (a.size() == 1 && !a[0]);
   }

   bigint operator-() const {
      bigint res = *this;
      res.sign = -sign;
      return res;
   }

   bigint abs() const {
      bigint res = *this;
      res.sign *= res.sign;
      return res;
   }

   long long longValue() const {
      long long res = 0;
      for (int i = a.size() - 1; i >= 0; i--)
         res = res * base + a[i];
      return res * sign;
   }

   friend bigint gcd(const bigint &a, const bigint &b) {
      return b.isZero() ? a : gcd(b, a % b);
   }
   friend bigint lcm(const bigint &a, const bigint &b) {
      return a / gcd(a, b) * b;
   }

   void read(const string &s) {
      sign = 1;
      a.clear();
      int pos = 0;
      while (pos < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) {
         if (s[pos] == '-')
            sign = -sign;
         ++pos;
      }
      for (int i = s.size() - 1; i >= pos; i -= base_digits) {
         int x = 0;
         for (int j = max(pos, i - base_digits + 1); j <= i; j++)
            x = x * 10 + s[j] - '0';
         a.push_back(x);
      }
      trim();
   }

   friend istream& operator>>(istream &stream, bigint &v) {
      string s;
      stream >> s;
      v.read(s);
      return stream;
   }

   friend ostream& operator<<(ostream &stream, const bigint &v) {
      if (v.sign == -1)
         stream << '-';
      stream << (v.a.empty() ? 0 : v.a.back());
      for (int i = (int) v.a.size() - 2; i >= 0; --i)
         stream << setw(base_digits) << setfill('0') << v.a[i];
      return stream;
   }

   static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
      vector<long long> p(max(old_digits, new_digits) + 1);
      p[0] = 1;
      for (int i = 1; i < (int) p.size(); i++)
         p[i] = p[i - 1] * 10;
      vector<int> res;
      long long cur = 0;
      int cur_digits = 0;
      for (int i = 0; i < (int) a.size(); i++) {
         cur += a[i] * p[cur_digits];
         cur_digits += old_digits;
         while (cur_digits >= new_digits) {
            res.push_back(int(cur % p[new_digits]));
            cur /= p[new_digits];
            cur_digits -= new_digits;
         }
      }
      res.push_back((int) cur);
      while (!res.empty() && !res.back())
         res.pop_back();
      return res;
   }

   typedef vector<long long> vll;

   static vll karatsubaMultiply(const vll &a, const vll &b) {
      int n = a.size();
      vll res(n + n);
      if (n <= 32) {
         for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++)
               res[i + j] += a[i] * b[j];
            return res;
      }

      int k = n >> 1;
      vll a1(a.begin(), a.begin() + k);
      vll a2(a.begin() + k, a.end());
      vll b1(b.begin(), b.begin() + k);
      vll b2(b.begin() + k, b.end());

      vll a1b1 = karatsubaMultiply(a1, b1);
      vll a2b2 = karatsubaMultiply(a2, b2);

      for (int i = 0; i < k; i++)
         a2[i] += a1[i];
      for (int i = 0; i < k; i++)
         b2[i] += b1[i];

      vll r = karatsubaMultiply(a2, b2);
      for (int i = 0; i < (int) a1b1.size(); i++)
         r[i] -= a1b1[i];
      for (int i = 0; i < (int) a2b2.size(); i++)
         r[i] -= a2b2[i];

      for (int i = 0; i < (int) r.size(); i++)
         res[i + k] += r[i];
      for (int i = 0; i < (int) a1b1.size(); i++)
         res[i] += a1b1[i];
      for (int i = 0; i < (int) a2b2.size(); i++)
         res[i + n] += a2b2[i];
      return res;
   }

   bigint operator*(const bigint &v) const {
      vector<int> a6 = convert_base(this->a, base_digits, 6);
      vector<int> b6 = convert_base(v.a, base_digits, 6);
      vll a(a6.begin(), a6.end());
      vll b(b6.begin(), b6.end());
      while (a.size() < b.size())
         a.push_back(0);
      while (b.size() < a.size())
         b.push_back(0);
      while (a.size() & (a.size() - 1))
         a.push_back(0), b.push_back(0);
      vll c = karatsubaMultiply(a, b);
      bigint res;
      res.sign = sign * v.sign;
      for (int i = 0, carry = 0; i < (int) c.size(); i++) {
         long long cur = c[i] + carry;
         res.a.push_back((int) (cur % 1000000));
         carry = (int) (cur / 1000000);
      }
      res.a = convert_base(res.a, 6, base_digits);
      res.trim();
      return res;
   }
};

void preproc() { }

void solve()
{
   int n;
   cin >> n;

   bigint dp[3*n+1][n+1][n+1][n+1][3];
   // dp[steps][x][y][z][last]

   dp[1][1][0][0][0] = 1;

   for (int steps = 1; steps <= 3*n; ++steps)
      for (int x = 0; x <= n; ++x)
         for (int y = 0; y <= n; ++y)
            for (int z = 0; z <= n; ++z)
               for (int last = 0; last <= 2; ++last)
                  if ( dp[steps][x][y][z][last] != 0 )
                     for (int j = 1; j <= 2; ++j) {
                        int next = (last + j) % 3;
                        int xx = (x + (next == 0));
                        int yy = (y + (next == 1));
                        int zz = (z + (next == 2));
                        if (xx > n or yy > n or zz > n)
                           continue;
                        dp[steps+1][xx][yy][zz][next] +=
                        dp[steps][x][y][z][last];
                        debug(xx, yy, zz, dp[steps+1][xx][yy][zz][next] );
                     }

   bigint n_fac = 1;
   for (int i = 2; i <= n; ++i)
      n_fac *= i;

   bigint perm = n_fac * n_fac * n_fac;
   // HOW TO GET THE RESULT ? COMBINATORICS STUFF
   cout << (dp[3*n][n][n][n][1])*perm / 2 << '\n';
}

signed main()
{
   IOS; PREC;
   preproc();

   int tc = 1;
   // cin >> tc;
   for (int Tt = 1; Tt <= tc; ++Tt) {
      // debug(Tt);
      // cout << "Case #" << Tt << ": ";
      solve();
   }
   return EXIT_SUCCESS;
}