#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <tuple>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
class TreeAndPathLength3 { public:
vector <int> construct(int s)
{
if(s == 1) {
int ans[] = {0, 1, 1, 2, 2, 3};
return vector<int>(ans+0, ans+6);
}
// . - . - . - . -.-.
// n nodes -.-.
// -.-.
// -.-. k branches
// =
// (n-3) + k + k + k(k-1)
int k=0;
for(; k+k+k*(k-1)<=s; ++k) {}
--k;
int n = s - k - k - k*(k-1) + 3;
vector<int> edges;
for(int v=0; v<n-1; ++v) {
edges.emplace_back(v);
edges.emplace_back(v+1);
}
for(int u=0; u<k; ++u) {
edges.emplace_back(n-1);
edges.emplace_back(n+u);
edges.emplace_back(n+u);
edges.emplace_back(n+u+k);
}
return edges;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const vector <int>& Expected, const vector <int>& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: " << Expected << endl << "\tx: " << Received << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, TreeAndPathLength3().construct(s));}
int main(){
CASE(0)
int s = 1;
int __[] = {0, 1, 1, 2, 2, 3 };
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(1)
int s = 2;
int __[] = {0, 1, 1, 2, 2, 3, 3, 4 };
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(2)
int s = 6;
int __[] = {0, 1, 1, 2, 0, 3, 3, 4, 0, 5, 5, 6 };
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(3)
int s = 8;
int __[] = {0, 1, 1, 2, 1, 3, 3, 4, 3, 5, 5, 6, 5, 7 };
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(4)
int s = 10000;
int __[] = {1};
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
/*
CASE(5)
int s = ;
int __[] = ;
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
*/
}
// END CUT HERE