#include "migrations.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
using pi = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vi>;
void dfs(int u, int p, vi &dist, vvi &adj) {
for (auto &v : adj[u]) {
if (v == p) continue;
dist[v] = dist[u] + 1;
dfs(v, u, dist, adj);
}
}
int furthest_from(int u, int n, vvi &adj) {
vector<int> dist(n);
dfs(u, u, dist, adj);
int f = 0; for (int i = 0; i < n; i++) if (dist[i] > dist[f]) f = i;
return f;
}
int dist_between(int n, int u, int v, vvi &adj) {
vector<int> dist(n);
dfs(u, u, dist, adj);
return dist[v];
}
pi furthest_pair(int n, vvi &adj) {
vector<int> dist(n);
dfs(0, 0, dist, adj);
int f1 = 0; for (int i = 0; i < n; i++) if (dist[i] > dist[f1]) f1 = i;
dist = vi(n, 0);
dfs(f1, f1, dist, adj);
int f2 = 0; for (int i = 0; i < n; i++) if (dist[i] > dist[f2]) f2 = i;
return {min(f1, f2), max(f1, f2)};
}
vi to_base(ll A, ll b, int pad = 0) {
vi ans;
while (A > 0LL) {
ans.push_back(A % b);
A /= b;
}
while (ans.size() < pad) ans.push_back(0);
return ans;
}
ll from_base(vi bx, ll b) {
ll po = 1;
ll ans = 0;
for (auto &el : bx) {
ans += ll(el) * po;
po *= b;
}
return ans;
}
const int CN = 12, CK = 3;
map<int, pair<int, uint64_t>> rank_to_mask;
map<pair<int, uint64_t>, int> mask_to_rank;
void initialise_ranks(int N, int K) {
rank_to_mask.clear(); mask_to_rank.clear();
uint64_t initial = 0;
int counter = 0;
auto dfs = [&](const auto &self, int type, uint64_t cur, int idx, int rem) {
if (rem == 0) {
rank_to_mask[counter] = {type, cur};
mask_to_rank[{type, cur}] = counter++;
return;
}
for (int i = idx; i < N; i++) {
uint64_t nxt = cur | (1LL << i);
self(self, type, nxt, i+1, rem-1);
}
};
for (int i = 0; i < 64; i++) {
dfs(dfs, i, initial, 0, K);
}
}
vvi adj;
pi fr;
int diam = 0, cpos = 0;
int U = 0, V = 0, rU = 0, rV = 0;
vector<int> change_types;
int x = 0, actual_step = 0;
bool changed = false;
int send_message(int n, int i, int Pi) {
if (i <= 1) {
adj.assign(n+1, vi());
initialise_ranks(CN, CK);
}
x = n - 32;
adj[Pi].push_back(i);
adj[i].push_back(Pi);
if (i < x) return 0;
int step = actual_step++;
if (step == 0) {
fr = furthest_pair(n, adj); diam = dist_between(n, fr.first, fr.second, adj);
U = fr.first; V = fr.second;
rU = U, rV = V;
} else if (step == 14) {
rV = V = furthest_from(U, n, adj);
}
pi cfr = furthest_pair(n, adj);
int u = cfr.first, v = cfr.second;
int cdiam = dist_between(n, u, v, adj);
int type = cdiam == diam ? 0 : (dist_between(n, i, V, adj) == cdiam ? 1 : 2); // if the diameter changed, did we switch u or v
change_types.push_back(type);
diam = cdiam;
if (type == 1) {
U = i;
} else if (type == 2) {
V = i;
if (step < 14) U = V;
}
// cout << "Step: " << step << " U: " << U << " V: " << V << "\n";
vi u12 = to_base(rU, 12, 4), v2 = to_base(rV, 2, 14);
auto mask1 = rank_to_mask[rU];
vector<int> umask(12, 0);
int ones_seen = 0; for (int i = 0; i < 12; i++) {
if (!(mask1.second & (1LL << i))) continue;
vi l4 = to_base(mask1.first, 4, 3);
umask[i] = l4[ones_seen]+1;
ones_seen++;
}
auto mask2 = rank_to_mask[rV];
vector<int> vmask(12, 0);
ones_seen = 0; for (int i = 0; i < 12; i++) {
if (!(mask2.second & (1LL << i))) continue;
vi l4 = to_base(mask2.first, 4, 3);
vmask[i] = l4[ones_seen]+1;
ones_seen++;
}
// cout << "mask1 - f: " << mask1.first << " s: "; for (int idx = 0; idx < 12; idx++) cout << min(1UL, mask1.second & (1 << idx)) << " "; cout << "\n";
// cout << "mask2 - f: " << mask2.first << " s: "; for (int idx = 0; idx < 12; idx++) cout << min(1UL, mask2.second & (1 << idx)) << " "; cout << "\n";
if (step < 12) {
return umask[step];
} else if (step < 14) {
int px = 14; for (int k = 0; k < 12; k++) if (change_types[k] != 0) px = k;
int a = px / 3, b = px % 3;
if (step == 12) return a;
else if (change_types[13] != 0) return 4;
else if (change_types[12] != 0) return 3;
else return b;
} else if (step < 26) {
return vmask[step - 14];
} else if (step < 28) {
int px = 14; for (int k = 0; k < 12; k++) if (change_types[14+k] == 1) px = k;
int a = px / 3, b = px % 3;
if (step == 26) return a;
else if (change_types[27] == 1) return 4;
else if (change_types[26] == 1) return 3;
else return b;
} else if (step < 30) {
int px = 14; for (int k = 0; k < 14; k++) if (change_types[14+k] == 2) px = k;
int a = px / 3, b = px % 3;
if (step == 28) return a;
else if (change_types[29] == 2) return 4;
else if (change_types[28] == 2) return 3;
else return b;
} else if (step == 30) {
if (change_types[28] == 1 && change_types[29] != 1) {
if (type == 0) return 3;
else if (type == 1) return 1; // double overlap = kill this state
else return 4;
} else {
if (type == 0) return 0;
else if (type == 1) return 1;
else return 2;
}
} else if (step == 31) {
if (change_types[29] == 1 && change_types[30] != 1) {
if (type == 0) return 3;
else if (type == 1) return 1; // double overlap = kill this state
else return 4;
} else {
if (type == 0) return 0;
else if (type == 1) return 1;
else return 2;
}
} else {
return 0; // shouldn't happen
}
}
// 0 - no change, 1 - change u, 2 - change v
pi longest_path(vi S) {
initialise_ranks(CN, CK);
int n = S.size();
int x = n - 32;
pair<int, uint64_t> mask1 = {0, 0}, mask2 = {0, 0};
vector<int> l4, c4;
for (int i = 0; i < 12; i++) {
if (S[x+i] == 0) continue;
mask1.second |= (1LL << i);
l4.push_back(S[x+i]-1);
}
for (int i = 14; i < 26; i++) {
if (S[x+i] == 0) continue;
mask2.second |= (1LL << (i - 14));
c4.push_back(S[x+i]-1);
}
mask1.first = from_base(l4, 4);
mask2.first = from_base(c4, 4);
// cout << "mask1 - f: " << mask1.first << " s: "; for (int idx = 0; idx < 12; idx++) cout << min(1UL, mask1.second & (1 << idx)) << " "; cout << "\n";
// cout << "mask2 - f: " << mask2.first << " s: "; for (int idx = 0; idx < 12; idx++) cout << min(1UL, mask2.second & (1 << idx)) << " "; cout << "\n";
int u = mask_to_rank[mask1], v = mask_to_rank[mask2];
if (S[x+13] == 3) u = x+12;
else if (S[x+13] == 4) u = x+13;
else if (!(S[x+12] == 4 && S[x+13] == 2)) u = x + (S[x+12] * 3 + S[x+13]);
if (S[x+27] == 3) u = x+26;
else if (S[x+27] == 4) u = x+27;
else if (!(S[x+26] == 4 && S[x+27] == 2)) u = x + 14 + (S[x+26] * 3 + S[x+27]);
if (S[x+29] == 3) v = x+28;
else if (S[x+29] == 4) v = x+29;
else if (!(S[x+28] == 4 && S[x+29] == 2)) v = x + 14 + (S[x+28] * 3 + S[x+29]);
if (S[x+30] == 0) {}
else if (S[x+30] == 1) u = x + 30;
else if (S[x+30] == 2) v = x + 30;
else if (S[x+30] == 3) u = x + 28;
else if (S[x+30] == 4) {u = x + 28; v = x + 30;}
if (S[x+31] == 0) {}
else if (S[x+31] == 1) u = x + 31;
else if (S[x+31] == 2) v = x + 31;
else if (S[x+31] == 3) u = x + 29;
else if (S[x+31] == 4) {u = x + 29; v = x + 31;}
// if (S[x+30] == 1) u = x + 29;
// else if (S[x+30] == 2) u = x + 28;
// else if (S[x+30] == 3) {v = x+30; u = x+29;}
// else if (S[x+30] == 4) {v = x+30; u = x+28;}
// if (S[x+31] == 0) u = x+30;
// else if (S[x+31] == 2) u = x+31;
// else if (S[x+31] == 3) {v = x+31; u = x+30;}
// else if (S[x+31] == 4) v = x+31;
// if (S[x+32] == 0) v = x+30;
// else if (S[x+32] == 2 && v != x + 31) {u = x+32; v = x+30;}
// else if (S[x+32] == 3) u = x+32;
// else if (S[x+32] == 4) v = x+32;
// auto bp = furthest_pair(n, adj);
// if (!(dist_between(n, u, v, adj) == dist_between(n, bp.first, bp.second, adj))) {
// cout << "failure!\n";
// }
int A = u, B = v;
return {A, B};
}
