#include "migrations.h"
#include "bits/stdc++.h"
using namespace std;
vector<pair<int, int>> m;
vector<vector<int>> adj;
vector<int> pow5;
int c1, c2;
int d1, d2;
#define upd {adj[i].push_back(Pi); adj[Pi].push_back(i);}
#define P(k, l) (u == k && v == l)
#define Q(k, l) ((d1 == k && d2 == l) || (d1 == l && d2 == k))
const int p = 9994, q = 9995, r = 9996;;
const int a = 9997, b = 9998, c = 9999;
int A, B, C;
void dfs(int cur, int par, vector<vector<int>>& adj, vector<int>& depth, int dep){
depth[cur] = dep;
for (auto &e: adj[cur]) if (e != par) dfs(e, cur, adj, depth, dep + 1);
}
pair<int, int> diameter(){
vector<int> depth(10000, 0), depth2(10000, 0);
dfs(0, -1, adj, depth, 0);
int max_depth = 0, end1 = -1, end2 = -1;
for (int i = 0; i < 10000; i++)
if (depth[i] > max_depth)
max_depth = depth[i], end1 = i;
max_depth = 0;
dfs(end1, -1, adj, depth2, 0);
for (int i = 0; i < 10000; i++)
if (depth2[i] > max_depth)
max_depth = depth2[i], end2 = i;
if (end1 > end2) swap(end1, end2);
return {end1, end2};
}
vector<int> encode(int x, int len){
vector<int> v(len);
int num = x;
for (int i = len - 1; i >= 0; i--){
int d = num/pow5[i];
v[i] = d;
num -= d * pow5[i];
}
return v;
}
int decode(vector<int> x){
int len = x.size();
int ans = 0;
for (int i = len - 1; i >= 0; i--){
int d = x[i];
ans += d * pow5[i];
}
return ans;
}
int encode12(int a, int b){
for (int i = 0; i < 66; i++)
if (m[i].first == a && m[i].second == b)
return i;
return -1;
}
pair<int, int> decode12(int x){
return m[x];
}
void pre(){
pow5.resize(12, 1);
for (int i = 1; i < 12; i++) pow5[i] = pow5[i-1] * 5;
c1 = -1, c2 = -1;
d1 = -1, d2 = -1;
A = -1, B = -1, C = -1;
m.clear();
for (int i = 0; i < 11; i++){
for (int j = i + 1; j < 12; j++){
m.push_back({i, j});
}
}
adj.resize(10000, vector<int>());
}
void one(int x, int y){
if (d1 == x && d2 == y) C = 0;
else if (d1 == x) C = 1;
else C = 2;
}
void rone(int x, int y){
if (C == 0) d1 = x, d2 = y;
else if (C == 1) d1 = x, d2 = c;
else d1 = y, d2 = c;
}
void two(int x, int y, int v){
if (d2 != c){
if (Q(x,v)) C = 0;
if (Q(y,v)) C = 1;
} else {
if (d1 == x) C = 2;
if (d1 == y) C = 3;
if (d1 == v) C = 4;
}
}
void rtwo(int x, int y, int v){
if (C == 0) d1 = min(x, v), d2 = max(x, v);
if (C == 1) d1 = min(y, v), d2 = max(y, v);
if (C == 2) d1 = x, d2 = c;
if (C == 3) d1 = y, d2 = c;
if (C == 4) d1 = v, d2 = c;
}
int send_message(int N, int i, int Pi) {
if (i == 1) pre();
if (i <= 9981){
upd;
return 0;
}
if (i <= 9993){
if (c1 == -1){
int u, v;
tie(u, v) = diameter();
c1 = u, c2 = v;
}
upd;
int V = 9999*c1 + c2;
vector<int> enc = encode(V, 12);
if (enc[i-9982] >= 5 || enc[i-9982] < 0) return 0;
else return enc[i - 9982];
}
if (i <= 9996){
if (d1 == -1){
int u, v;
tie(u, v) = diameter();
d1 = u, d2 = v;
}
upd;
int V;
if (c1 == d1 && c2 == d2) V = 124;
else if (c1 == d1) V = 70 + d2 - 9982;
else if (d1 == c2) V = 90 + d2 - 9982;
else V = encode12(d1 - 9982, d2 - 9982);
vector<int> enc = encode(V, 3);
if (i == 9996) c1 = d1, c2 = d2;
if (enc[i-9994] >= 5 || enc[i-9994] < 0) return 0;
else return enc[i - 9994];
}
if (i == a) {
upd;
int u, v;
tie(u, v) = diameter();
A = 4;
if (P(c1, c2) || P(c1, p) || P(c1, q)) A = 0;
if (P(c1, r) || P(c1, a) || P(c2, p)) A = 1;
if (P(c2, q) || P(c2, r) || P(c2, a)) A = 2;
if (P(p, q) || P(p, r) || P(p, a)) A = 3;
if (P(q, r) || P(q, a) || P(r, a)) A = 4;
return A;
}
if (i == b) {
upd;
int u, v;
tie(u, v) = diameter();
B = 4;
if (A == 0){
if (P(c1, c2)) B = 0;
if (P(c1, p)) B = 1;
if (P(c1, q)) B = 2;
if (P(c1, b) || P(c2, b)) B = 3;
if (P(p, b) || P(q, b)) B = 4;
}
if (A == 1){
if (P(c1, r)) B = 0;
if (P(c1, a) || P(c1, b)) B = 1;
if (P(c2, p)) B = 2;
if (P(c2, b) || P(r, b)) B = 3;
if (P(p, b) || P(a, b)) B = 4;
}
if (A == 2){
if (P(c2, q)) B = 0;
if (P(c2, r)) B = 1;
if (P(c2, a)) B = 2;
if (P(c2, b) || P(q, b)) B = 3;
if (P(r, b) || P(a, b)) B = 4;
}
if (A == 3){
if (P(p, q)) B = 0;
if (P(p, r)) B = 1;
if (P(p, a)) B = 2;
if (P(p, b) || P(q, b)) B = 3;
if (P(r, b) || P(a, b)) B = 4;
}
if (A == 4){
if (P(q, r)) B = 0;
if (P(q, a)) B = 1;
if (P(r, a)) B = 2;
if (P(q, b)) B = 3;
if (P(r, b) || P(a, b)) B = 4;
}
d1 = u, d2 = v;
return B;
}
upd;
int u = d1, v = d2;
tie(d1, d2) = diameter();
C = 0;
if (A == 0){
if (P(c1, c2)) one(c1, c2);
if (P(c1, p)) one(c1, p);
if (P(c1, q)) one(c1, q);
if (P(c1, b) || P(c2, b)) two(c1, c2, b);
if (P(p, b) || P(q, b)) two(p, q, b);
}
if (A == 1){
if (P(c1, r)) one(c1, r);
if (P(c1, a) || P(c1, b)) two(a, b, c1);
if (P(c2, p)) one(c2, p);
if (P(c2, b) || P(r, b)) two(c2, r, b);
if (P(p, b) || P(a, b)) two(p, a, b);
}
if (A == 2){
if (P(c2, q)) one(c2, q);
if (P(c2, r)) one(c2, r);
if (P(c2, a)) one(c2, a);
if (P(c2, b) || P(q, b)) two(c2, q, b);
if (P(r, b) || P(a, b)) two(r, a, b);
}
if (A == 3){
if (P(p, q)) one(p, q);
if (P(p, r)) one(p, r);
if (P(p, a)) one(p, a);
if (P(p, b) || P(q, b)) two(p, q, b);
if (P(r, b) || P(a, b)) two(r, a, b);
}
if (A == 4){
if (P(q, r)) one(q, r);
if (P(q, a)) one(q, a);
if (P(r, a)) one(r, a);
if (P(q, b)) one(q, b);
if (P(r, b) || P(a, b)) two(r, a, b);
}
return C;
}
pair<int, int> longest_path(vector<int> S) {
pre();
vector<int> part1(12);
for (int i = 9982; i <= 9993; i++) part1[i - 9982] = S[i];
int V = decode(part1);
int C1 = (V - V%c)/c, C2 = V%c;
vector<int> part2(3);
for (int i = p; i <= r; i++) part2[i - p] = S[i];
V = decode(part2);
if (V <= 67){
int u, v;
tie(u, v) = decode12(V);
C1 = u + 9982, C2 = v + 9982;
} else if (V < 90) {
C2 = V + 9982 - 70;
} else if (V < 120){
C1 = V + 9982 - 90;
swap(C1, C2);
} else {
// C1, C2 unchanged
}
A = S[a], B = S[b], C = S[c];
d1 = -1, d2 = -1;
if (A == 0){
if (B == 0) rone(C1, C2);
if (B == 1) rone(C1, p);
if (B == 2) rone(C1, q);
if (B == 3) rtwo(C1, C2, b);
if (B == 4) rtwo(p, q, b);}
if (A == 1){
if (B == 0) rone(C1, r);
if (B == 1) rtwo(a, b, C1);
if (B == 2) rone(C2, p);
if (B == 3) rtwo(C2, r, b);
if (B == 4) rtwo(p, a, b);}
if (A == 2){
if (B == 0) rone(C2, q);
if (B == 1) rone(C2, r);
if (B == 2) rone(C2, a);
if (B == 3) rtwo(C2, q, b);
if (B == 4) rtwo(r, a, b);}
if (A == 3){
if (B == 0) rone(p, q);
if (B == 1) rone(p, r);
if (B == 2) rone(p, a);
if (B == 3) rtwo(p, q, b);
if (B == 4) rtwo(r, a, b);}
if (A == 4){
if (B == 0) rone(q, r);
if (B == 1) rone(q, a);
if (B == 2) rone(r, a);
if (B == 3) rone(q, b);
if (B == 4) rtwo(r, a, b);}
return {d1, d2};
}
