#include "scales.h"
#include <algorithm>
#include <stdio.h>
#include <vector>

namespace
{

typedef long long llt;
typedef unsigned uint;typedef unsigned long long ullt;
typedef bool bol;typedef char chr;typedef void voi;
typedef double dbl;
template<typename T>bol _max(T&a,T b){return(a<b)?a=b,true:false;}
template<typename T>bol _min(T&a,T b){return(b<a)?a=b,true:false;}
template<typename T>T lowbit(T n){return n&-n;}
template<typename T>T gcd(T a,T b){return b?gcd(b,a%b):a;}
template<typename T>T lcm(T a,T b){return(a!=0||b!=0)?a/gcd(a,b)*b:(T)0;}
template<typename T>T exgcd(T a,T b,T&x,T&y){if(b!=0){T ans=exgcd(b,a%b,y,x);y-=a/b*x;return ans;}else return y=0,x=1,a;}
template<typename T>T power(T base,T index,T mod)
{
    T ans=1%mod;
    while(index)
    {
        if(index&1)ans=ans*base%mod;
        base=base*base%mod,index>>=1;
    }
    return ans;
}

uint Per[805][6],Ans[805][125];
uint Son[3][2005],Now[2005],tp;
uint X[125],Y[125],Z[125],W[125];

bol build(std::vector<uint>V,uint s)
{
    if(V.empty())return true;
    // printf("%u %u\n",(uint)V.size(),s);
    uint t=tp++;
    if(V.size()==1)return Now[t]=-1,Son[0][t]=V[0],true;
    s/=3;
    for(uint&e=Now[t]=0;e<120;e++)
    {
        std::vector<uint>S[3];for(auto j:V)S[Ans[j][e]].push_back(j);
        // printf("%u %u %u\n",(uint)X[0].size(),(uint)X[1].size(),(uint)X[2].size());
        if(S[0].size()<=s&&S[1].size()<=s&&S[2].size()<=s&&
            (Son[0][t]=tp,build(S[0],s))&&(Son[1][t]=tp,build(S[1],s))&&(Son[2][t]=tp,build(S[2],s)))
            return true;
        tp=t+1;
    }
    return false;
}

voi output(uint id)
{
    static int P[6];
    for(uint i=0;i<6;i++)
        P[i]=Per[id][i]+1;
    answer(P);
}

voi bzr()
{
    for(uint i=0;i<6;i++)Per[0][i]=i;
    for(uint i=1;i<720;i++)
    {
        for(uint j=0;j<6;j++)Per[i][j]=Per[i-1][j];
        std::next_permutation(Per[i],Per[i]+6);
    }
    for(uint i=0,t=0;i<6;i++)for(uint j=0;j<i;j++)for(uint k=0;k<j;k++)
        X[t+40]=X[t+20]=X[t]=i,Y[t+40]=Y[t+20]=Y[t]=j,Z[t+40]=Z[t+20]=Z[t]=k,t++;
    for(uint i=0,t=60;i<6;i++)for(uint j=0;j<i;j++)for(uint k=0;k<j;k++)
        for(uint l=0;l<6;l++)if(i!=l&&j!=l&&k!=l)
            X[t]=i,Y[t]=j,Z[t]=k,W[t]=l,t++;
    std::vector<uint>V;
    for(uint i=0;i<720;i++)
    {
        V.push_back(i);
        for(uint j=0;j<20;j++)for(uint k=0,t=0;k<6;k++)if(Per[i][k]==X[j]||Per[i][k]==Y[j]||Per[i][k]==Z[j])
            Ans[i][t++*20+j]=Per[i][k]==Z[j]?2:Per[i][k]==Y[j];
        for(uint p=60;p<120;p++)for(uint j=0;j<6;j++)if(Per[i][j]==W[p])
        {
            uint w=-1;
            for(uint k=j+1;!~w;k=(k+1)%6)if(Per[i][k]==X[p]||Per[i][k]==Y[p]||Per[i][k]==Z[p])w=Per[i][k];
            Ans[i][p]=w==Z[p]?2:w==Y[p];
            // printf("%u %u\n",p,w);
        }
    }
    if(!build(V,729))
        puts("qwq"),exit(233);
    // exit(0);
}

voi solve()
{
    uint t=0;
    while(~Now[t])
    {
        if(Now[t]<60)
        {
            uint op=Now[t]/20,x=X[Now[t]]+1,y=Y[Now[t]]+1,z=Z[Now[t]]+1;
            uint v=(op?op==2?getHeaviest:getMedian:getLightest)(x,y,z);
            t=Son[v==z?2:v==y][t];
        }
        else
        {
            uint x=X[Now[t]]+1,y=Y[Now[t]]+1,z=Z[Now[t]]+1,w=W[Now[t]]+1;
            uint v=getNextLightest(x,y,z,w);
            t=Son[v==z?2:v==y][t];
        }
    }
    output(Son[0][t]);
}

}

void init(int T)
{
    bzr();
}

void orderCoins()
{
    solve();
}

/*

g++ 230.cpp grader.cpp -o code -std=c++11

*/

answer.code:1:10: fatal error: scales.h: No such file or directory
    1 | #include "scales.h"
      |          ^~~~~~~~~~
compilation terminated.