#include "Anna.h"
#include <bits/stdc++.h>
using namespace std;
namespace{
#ifdef zisk
void debug(){cout << endl;}
template<class T, class ... U> void debug(T a, U ... b){cout << a << " ", debug(b...);}
template<class T> void pary(T l, T r) {
while (l != r) cout << *l << " ", l++;
cout << endl;
}
#else
#define debug(...) 0
#define pary(...) 0
#endif
#define ll long long
#define maxn 200005
#define pii pair<int, int>
#define ff first
#define ss second
#define io ios_base::sync_with_stdio(0);cin.tie(0);
ll po(ll a, ll n) {
ll ret = 1;
while (n) {
if (n & 1) ret = ret * a;
n >>= 1;
a = a * a;
}
return ret;
}
vector<int> adj[200000];
vector<int> build_path() {
int n = 10;
auto good = [&] (ll x) {
for (int i = 0;i < n;i++) {
if (x % 3 == 0) return true;
x /= 3;
}
return false;
};
ll m = po(3, n);
for (int i = 0;i < m;i++) {
for (int j = 0;j < 3;j++) {
int to = (i * 3 + j) % m;
if (!good(i) && j != 0) continue;
if (i == 0 && j == 0) continue;
adj[i].push_back(to);
}
}
vector<int> path, stk;
int cur = 0;
stk.push_back(cur);
while (stk.size()) {
cur = stk.back();
int tmp = cur;
while (adj[cur].size()) {
int v = adj[cur].back();
adj[cur].pop_back();
cur = v;
stk.push_back(v);
break;
}
if (tmp != cur) continue;
path.push_back(cur);
stk.pop_back();
}
reverse(path.begin(), path.end());
return path;
}
int to_int(char c) {
if (c == 'R') return 0;
else if (c == 'G') return 1;
else return 2;
}
char to_char(int i) {
const string S = "RGB";
return S[i];
}
int add_diff(int prv, int res) {
if ((prv+1)%3 != res) return (prv+1)%3;
else return (prv+2)%3;
}
void add_bit(std::vector<int> &ret, std::vector<int> &v, int bit) {
//add semantic bit, could be 0/1/2, which takes up v[ind] and v[ind+1]
int ind = ret.size();
if (ind >= v.size()) return;
if (ind + 1 >= v.size()) {
ret.push_back(add_diff(ret.back(), v[ind]));
return;
}
int done = 0;
for (int i = 1;i < 3;i++) {
for (int j = 1;j < 3;j++) {
int vi = (v[ind] + i) % 3, vj = (v[ind+1] + j) % 3;
if ((vj - vi + 3) % 3 == bit) {
ret.push_back(vi);
ret.push_back(vj);
done = 1;
break;
}
}
if (done) break;
}
ind = ret.size();
if (ind >= v.size()) return;
ret.push_back(add_diff(ret.back(), v[ind]));
}
}
pair<string, int> anna(int N, string S) {
vector<int> v(N, 0), ret;
for (int i = 0;i < N;i++) v[i] = to_int(S[i]);
ret.push_back((v[0] + 1) %3);
vector<int> nodes = build_path();
vector<int> dig;
for (int i = 0;i < 10;i++) add_bit(ret, v, 0), dig.push_back(0);
for (int i = 1;i < nodes.size();i++) {
if (ret.size() >= N) break;
add_bit(ret, v, nodes[i] % 3);
dig.push_back(nodes[i] % 3);
}
pary(dig.begin(), dig.end());
while (ret.size() >= N) ret.pop_back();
int L = min(N, 34);
string T;
for (int i = 0;i < N;i++) T.push_back(to_char(ret[i]));
return make_pair(T, L);
}
#include "Bruno.h"
#include <bits/stdc++.h>
using namespace std;
namespace{
#ifdef zisk
void debug(){cout << endl;}
template<class T, class ... U> void debug(T a, U ... b){cout << a << " ", debug(b...);}
template<class T> void pary(T l, T r) {
while (l != r) cout << *l << " ", l++;
cout << endl;
}
#else
#define debug(...) 0
#define pary(...) 0
#endif
#define ll long long
#define maxn 500005
#define pii pair<int, int>
#define ff first
#define ss second
#define io ios_base::sync_with_stdio(0);cin.tie(0);
int N, L;
ll po(ll a, ll n) {
ll ret = 1;
while (n) {
if (n & 1) ret = ret * a;
n >>= 1;
a = a * a;
}
return ret;
}
vector<int> adj[200000];
vector<int> build_path() {
int n = 10;
auto good = [&] (ll x) {
for (int i = 0;i < n;i++) {
if (x % 3 == 0) return true;
x /= 3;
}
return false;
};
ll m = po(3, n);
for (int i = 0;i < m;i++) {
for (int j = 0;j < 3;j++) {
int to = (i * 3 + j) % m;
if (!good(i) && j != 0) continue;
if (i == 0 && j == 0) continue;
adj[i].push_back(to);
}
}
vector<int> path, stk;
int cur = 0;
stk.push_back(cur);
while (stk.size()) {
cur = stk.back();
int tmp = cur;
while (adj[cur].size()) {
int v = adj[cur].back();
adj[cur].pop_back();
cur = v;
stk.push_back(v);
break;
}
if (tmp != cur) continue;
path.push_back(cur);
stk.pop_back();
}
reverse(path.begin(), path.end());
return path;
}
vector<int> path;
int edge_ind[maxn];
int to_int(char c) {
if (c == 'R') return 0;
else if (c == 'G') return 1;
else return 2;
}
}
void init(int N, int l) {
::N = N;
::L = l;
debug("L", l);
path = build_path();
for (int i = 1;i < path.size();i++) {
int val = path[i-1] * 3 + path[i] % 3;
assert(edge_ind[val] == 0);
edge_ind[val] = i;
}
}
int bruno(string s) {
if (N == L) return 1;
assert(s.size() == L);
vector<int> v[3];
bool has_zero[3] = {0, 0, 0};
for (int i = 1;i < L;i++) {
int a = to_int(s[i]), b = to_int(s[i-1]);
v[i%3].push_back((a - b + 3) % 3);
if (a == b) has_zero[i%3] = 1;
}
int col = 0;
for (int i = 0;i < 3;i++) {
if (has_zero[i] && !has_zero[(i+1)%3]) col = i;
}
assert(has_zero[0] || has_zero[1] || has_zero[2]);
assert(!has_zero[0] || !has_zero[1] || !has_zero[2]);
int num = 0;
for (int i:v[col]) {
num = num * 3 + i;
}
int pos = -1 + 3 * edge_ind[num];
pos += 1 - col;
if (col == 0) pos -= 3;
debug(num, edge_ind[num], col, pos);
//debug(num, col);
debug("Answer", pos);
return pos;
}
