#include "scales.h"
#include <bits/stdc++.h>
#define pb push_back
#define f first
#define sc second
using namespace std;
typedef long long int ll;
typedef string str;
void init(int T){
}
template<typename it, typename t>
void merge_sort(it l, it r, t && comp){
int n = r-l;
if(n <= 1) return;
int md = n/2;
merge_sort(l, l+md, comp);
merge_sort(l+md, r, comp);
typename remove_reference<decltype(*l)>::type* sth
= new typename remove_reference<decltype(*l)>::type[n];
for(int i = 0; i < n; i++) sth[i] = *(l+i);
merge(sth, sth+md, sth+md, sth+n, l, comp);
delete[] sth;
}
void orderCoins(){
int w[6] = {1, 2, 3, 4, 5, 6};
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
shuffle(w, w+6, rng);
vector<vector<bool>> c(7, vector<bool>(7, 0)), cc(7, vector<bool>(7, 0));
merge_sort(w, w+6, [&](int a, int b){
if(cc[a][b]) return bool(c[a][b]);
for(int i = 1; i <= 6; i++){
if(i == a || i == b) continue;
bool ok = 0, comp;
if(cc[a][i]){
ok = 1;
if(c[a][i]) comp = getLightest(a, b, i) == a;
else comp = getHeaviest(a, b, i) == b;
}
else if(cc[b][i]){
ok = 1;
if(c[b][i]) comp = getLightest(a, b, i) == a;
else comp = getHeaviest(a, b, i) == b;
}
if(ok){
cc[a][b] = 1, cc[b][a] = 1;
c[a][b] = comp;
c[b][a] = !comp;
return comp;
}
}
for(int _i = 0, i = w[_i]; _i <= 6; _i++, i = w[_i]) if(a != i && b != i){
bool bl = 0;
for(int j = 1; j <= 6; j++) if(j != i && cc[i][j]) bl = 1;
if(bl) continue;
int x = getLightest(a, b, i);
for(int y: vector<int>{a, b, i}) if(x != y){
cc[x][y] = 1, cc[y][x] = 1;
c[x][y] = 1, c[y][x] = 0;
}
if(x == a) return true;
if(x == b) return false;
x = getMedian(a, b, i);
cc[a][b] = 1, cc[b][a] = 1;
if(x == a){
c[a][b] = 1, c[b][a] = 0;
return true;
}
else{
c[a][b] = 0, c[b][a] = 1;
return false;
}
}
for(int _i = 0, i = w[_i]; _i <= 6; _i++, i = w[_i]) if(a != i && b != i){
int x = getLightest(a, b, i);
for(int y: vector<int>{a, b, i}) if(x != y){
cc[x][y] = 1, cc[y][x] = 1;
c[x][y] = 1, c[y][x] = 0;
}
if(x == a) return true;
if(x == b) return false;
x = getMedian(a, b, i);
cc[a][b] = 1, cc[b][a] = 1;
if(x == a){
c[a][b] = 1, c[b][a] = 0;
return true;
}
else{
c[a][b] = 0, c[b][a] = 1;
return false;
}
}
return false;
});
answer(w);
}
