#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 <cstring>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
class HeightRound { public:
typedef pair<pair<int,int>,int> key_t;
map<key_t, int> memo;
int score( int F, int B, int I, const vector<int>& h )
{
if( I == h.size()-1 )
return max(h[I]-h[F], h[I]-h[B]);
key_t key(make_pair(F,B), I);
if( memo.count(key) )
return memo[key];
int s1 = max(h[I]-h[F], score(I, B, I+1, h));
int s2 = max(h[I]-h[B], score(F, I, I+1, h));
return memo[key] = min(s1, s2);
}
void best( int F, int B, int I, const vector<int>& h, int acc, deque<int>& result )
{
if( I == h.size()-1 ) {
result = deque<int>(1, h[I]);
result.push_front(h[F]);
result.push_back(h[B]);
return;
}
int s1 = max(acc, max(h[I]-h[F], score(I, B, I+1, h)));
int s2 = max(acc, max(h[I]-h[B], score(F, I, I+1, h)));
if( s1<=s2 ) { // if tie, choose lexicographically earlier one
best( I, B, I+1, h, s1, result );
result.push_front( h[F] );
}
else {
best( F, I, I+1, h, s2, result );
result.push_back( h[B] );
}
}
vector <int> getBestRound(vector <int> h)
{
// The answer must be of form:
// h[0], h[1], (...ascending...), h[$-1], (...descending...).
// Thus, I begin from
// F=1, B=0: [h[1], .........., h[0]]
// and fill each h[I=2,3,...] either to the left or right of the blank space,
// and choose the best one. To choose lex-first candidate, I use the "jo-seki"
// technique, which first computes only scores and then choose the instance
// lexicographically afterwards.
sort(h.begin(), h.end());
deque<int> result;
best( 1, 0, 2, h, 0, result );
rotate(result.begin(), result.end()-1, result.end());
return vector<int>(result.begin(), result.end());
}
};
// 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(_, HeightRound().getBestRound(heights));}
int main(){
CASE(0)
int heights_[] = {1,2,3,4};
vector <int> heights(heights_, heights_+sizeof(heights_)/sizeof(*heights_));
int __[] = {1, 2, 4, 3 };
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(1)
int heights_[] = {1000,500,1};
vector <int> heights(heights_, heights_+sizeof(heights_)/sizeof(*heights_));
int __[] = {1, 500, 1000 };
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(2)
int heights_[] = {1,3,4,5,7};
vector <int> heights(heights_, heights_+sizeof(heights_)/sizeof(*heights_));
int __[] = {1, 3, 5, 7, 4 };
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(3)
int heights_[] = {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1};
vector <int> heights(heights_, heights_+sizeof(heights_)/sizeof(*heights_));
int __[] = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 };
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(4)
int heights_[] = {1,2,1};
vector <int> heights(heights_, heights_+sizeof(heights_)/sizeof(*heights_));
int __[] = {1,1,2};
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(5)
int heights_[] = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,1000};
vector <int> heights(heights_, heights_+sizeof(heights_)/sizeof(*heights_));
int __[] = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,1000,49};
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
CASE(6)
int heights_[] = {7, 43, 3, 6, 32, 2, 42, 23, 1, 30};
vector <int> heights(heights_, heights_+sizeof(heights_)/sizeof(*heights_));
int __[] = {1, 2, 3, 6, 7, 30, 32, 42, 43, 23};
vector <int> _(__, __+sizeof(__)/sizeof(*__));
END
}
// END CUT HERE