#include "migrations.h"
#include <bits/stdc++.h>
using namespace std;
#define forsn(i, s, n) for (int i = int(s); i < int(n); i++)
#define forn(i, n) forsn(i, 0, n)
#define dforsn(i, s, n) for (int i = int(n) - 1; i >= int(s); i--)
#define dforn(i, n) dforsn(i, 0, n)
using vi = vector<int>;
using ll = long long;
using ii = pair<int, int>;
#define fst first
#define snd second
#define sz(x) int(x.size())
#define all(x) begin(x), end(x)
#define pb push_back
#define eb emplace_back
const int N = 10000;
const int K = 15;
const int B = 7;
int up[K][N], depth[N];
int lca(int u, int v) {
if (depth[u] < depth[v]) swap(u, v);
int diff = depth[u] - depth[v];
forn(i, K) if (diff >> i & 1) u = up[i][u];
if (u == v) return u;
dforn(i, K) if (up[i][u] != up[i][v]) {
u = up[i][u], v = up[i][v];
}
assert(up[0][u] == up[0][v]);
return up[0][u];
}
int dist(int u, int v) {
return depth[u] + depth[v] - 2 * depth[lca(u, v)];
}
vi perm[N], invPerm[N];
void generate_perms() {
srand(2006);
vi p(5);
iota(all(p), 0);
forn(i, N) {
random_shuffle(all(p));
perm[i] = p;
vi inv_p(5);
forn(j, 5) inv_p[p[j]] = j;
invPerm[i] = inv_p;
}
}
int u, v;
int send_message(int /*N*/, int i, int Pi) {
if (i == 1) {
generate_perms();
depth[0] = 0;
forn(i, K) up[i][0] = 0;
u = 0, v = 0;
}
up[0][i] = Pi, depth[i] = depth[Pi] + 1;
forn(j, K - 1) up[j + 1][i] = up[j][up[j][i]];
int state = 0;
if (dist(i, v) > dist(u, v)) u = i, state = 1;
else if (dist(i, u) > dist(u, v)) v = i, state = 2;
if (i < N - 3 * B) return 0;
if (i >= N - 2 * B) {
if (state == 2) return perm[i][4];
int digit = v >> (i - (N - 2 * B)) & 1;
return perm[i][2 * state + digit];
}
if (state == 1) return perm[i][4];
return perm[i][u >> (2 * (i - (N - 3 * B))) & 3];
}
ii longest_path(vi S) {
generate_perms();
int U = 0, V = 0;
int lastU = -1, lastV = -1;
forsn(i, N - 3 * B, N - 2 * B) {
int x = invPerm[i][S[i]];
if (x == 4) lastU = i;
else U += x << (2 * (i - (N - 3 * B)));
}
forsn(i, N - 2 * B, N) {
int x = invPerm[i][S[i]];
if (x == 4) lastV = i;
else {
if (x >= 2) lastU = i;
V += (x & 1) << (i - (N - 2 * B));
}
}
if (lastU != -1) U = lastU;
if (lastV != -1) V = lastV;
return {U, V};
}
