#include "doll.h"
#include <bits/stdc++.h>
using namespace std;
struct tree {
int n, size;
vector<int> t, x, y, state;
void build(int N, int amt) {
n=N;
size=1;
while ((size<<1)<n) size<<=1;
t.assign(2*size-1,0), x.assign(2*size-1,0), y.assign(2*size-1,0), state.assign(2*size-1,0);
for (int i=1; i<=size-1; ++i) {
x[i-1] = -(2*i);
y[i-1] = -(2*i+1);
}
int cnt=0, p=0;
while (cnt<2*size-amt) {
if (p>=size-1) {
if (state[p]) {
y[p]=-1;
} else {
x[p]=-1;
}
state[p]^=1;
++cnt;
p=0;
continue;
}
if (!state[p]) {
state[p]^=1;
p<<=1; ++p;
} else {
state[p]^=1;
++p; p<<=1;
}
}
}
};
vector<vector<int>> solve1(int n, int m, vector<int>&a, vector<int>&cnt) {
vector<int> c(m+1),x,y;
c[0]=a[0];
vector<tree> v(m+1);
for (int i=1; i<=m; ++i) v[i].build(cnt[i],cnt[i]);
int in=0, p=0;
while (in<n) {
int ind = a[in];
while (p<v[ind].size-1) {
if (!v[ind].state[p]) {
v[ind].state[p]^=1;
p<<=1;
++p;
} else {
v[ind].state[p]^=1;
++p;
p<<=1;
}
}
if (!v[ind].state[p]) {
v[ind].x[p]= ((++in)<n) ? a[in] : 0;
v[ind].state[p]^=1;
} else {
v[ind].y[p]= ((++in)<n) ? a[in] : 0;
v[ind].state[p]^=1;
}
p=0;
}
for(int i=1; i<=m; ++i) {
int sz=x.size();
for (auto X:v[i].x) x.push_back( X>=0 ? X : (X-sz) );
for (auto Y:v[i].y) y.push_back( Y>=0 ? Y : (Y-sz) );
c[i]=-1-sz;
}
vector<vector<int>> r = {c,x,y};
return r;
}
vector<vector<int>> solve2(int n, int m, vector<int>&a) {
vector<int> c(m+1,-1), x, y; c[0]=a[0]; if (a.size()%2) a.push_back(-1); a.push_back(0);
int sz=1; while ((sz<<1)<n) sz<<=1;
int N=n+(n%2);
x.assign(sz-1,-1); y.assign(sz-1,-1);
for (int i=1; 2*i+1<=sz-1; ++i) {
x[i-1]=-(2*i); y[i-1]=-(2*i+1);
}
vector<int> state(2*sz-1,-1);
for (int i=0; i<sz-1; ++i) state[i]=0;
int cnt=0; int id=N;
while (cnt<2*sz) {
int p=0;
while (p<sz-1) {
if (state[p]==0) {
state[p]^=1;
p=p*2+2;
} else {
state[p]^=1;
p=p*2+1;
}
}
if (cnt%sz<N/2) {
if (state[p]==-1) {
int prv=(p-1)>>1;
if (state[prv]) y[prv]=-(y.size()+1);
else x[prv]=-(y.size()+1);
y.push_back(a[id--]);
state[p]=1;
} else {
x.push_back(a[id--]);
}
}
++cnt;
}
return {c,x,y};
}
void create_circuit(int m, vector<int>a) {
int n=a.size();
vector<int> cnt(m+1,0);
int mx=0;
for (int i=0; i<n; ++i) {
cnt[a[i]]++;
mx=max(mx,cnt[a[i]]);
}
if (mx==1) {
vector<int> c(m+1,0);
c[0]=a[0];
for (int i=1; i<n; ++i) {
c[a[i-1]]=a[i];
}
vector<int> x(0), y(0);
answer(c,x,y);
} else if (mx==2) {
vector<vector<int>> next(m+1);
//vector<int> b=a;
a.push_back(0);
for (int i=0; i<n; ++i) next[a[i]].push_back(a[i+1]);
vector<int> c(m+1);
c[0]=a[0];
for (int i=1; i<=m; ++i) {
c[i]=-i;
}
vector<int> x(m,0), y(m,0);
for (int i=1; i<=m; ++i) {
if (!next[i].size()) continue;
x[i-1] = next[i].size()>1 ? next[i][0] : -(i);
y[i-1] = next[i].size()>1 ? next[i][1] : next[i][0];
}
answer(c,x,y);
} else if (n==16) {
vector<int> c(m+1,-1); c[0]=a[0];
vector<int> x(15), y(15);
for (int i=0;i<7;++i) {x[i]=-(2*i+2); y[i]=-(2*i+3);}
x[7]=a[1], x[11]=a[2], x[9]=a[3], x[13]=a[4], x[8]=a[5], x[12]=a[6], x[10]=a[7], x[14]=a[8];
y[7]=a[9], y[11]=a[10], y[9]=a[11], y[13]=a[12], y[8]=a[13], y[12]=a[14], y[10]=a[15], y[14]=0;
answer(c,x,y);
} else if (m==1) {
int size=1;
while (4*size<n) size<<=1;
vector<int> x(2*size+1), y(2*size+1), state(2*size+1,0), c = {1, -(2*size)};
for (int i=1; i<=size-1; ++i) {
x[i-1] = -(2*i);
y[i-1] = -(2*i+1);
}
x[2*size-1]=-(2*size+1);
y[2*size-1]=-1;
x[2*size] = y[2*size] = 1;
int cnt=0, p=0;
while (cnt<2*size) {
//cout<<p<<"->";
if (p>=size-1) {
//cout<<"added "<<p<<' '<<cnt<<'\n';
if (state[p]) {
if (cnt<n-1-2*size) y[p]=1;
else y[p]=-(2*size);
} else {
if (cnt<n-1-2*size) x[p]=1;
else x[p]=-(2*size);
}
state[p]^=1;
++cnt;
p=0;
continue;
}
if (!state[p]) {
state[p]^=1;
p<<=1; ++p;
} else {
state[p]^=1;
++p; p<<=1;
}
}
y[2*size-2]=0;
answer(c,x,y);
} else {
vector<vector<int>> f = solve1(n,m,a,cnt);
vector<vector<int>> s = solve2(n,m,a); //cout<<f[0].size()<<' '<<f[1].size()<<' '<<f[2].size()<<'\n';
//for (auto x:f[1]) cout<<x<<' '; cout<<'\n';
//for (auto y:f[2]) cout<<y<<' '; cout<<'\n';
if (f[1].size()>s[1].size()) swap(f,s);
answer(f[0],f[1],f[2]);
}
}
