/// 407!3 +/ \!<07!\*
#include <bits/stdc++.h>
#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
using namespace std;
using ll = long long;
using db = long double; // or double, if TL is tight
using str = string; // yay python!
using pi = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
using vvi = vector<vi>;
using vvl = vector<vl>;
using vvpi = vector<vpi>;
template<class T> using pq = priority_queue<T>;
template<class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
// pairs
#define mp make_pair
#define f first
#define s second
// vectors
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pb push_back
#define eb emplace_back
#define pf push_front
#define er erase
#define ub upper_bound
#define lb lower_bound
// loops
#define FOR(i,a,b) for (ll i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (ll i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll INF = 1e18; // not too close to LLONG_MAX
const db PI = acos((db)-1);
const int dx[4] = {1,0,-1,0}, dy[4] = {0,1,0,-1}; // for every grid problem!
const char nl = '\n';
template<class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ", "; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? ", " : ""), __print(i); cerr << "}";}
void _print() {cerr << "\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<typename T>
using indexed_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define ook order_of_key
#define fbo find_by_order
void _input() {return;}
template <typename T, typename... V>
void _input(T &t, V&... v) {cin >> (t); if (sizeof...(v)) _input(v...);}
void __input(vi &v, const int n){F0R(i, n)cin >> v[i];}
void __input(vvi &v, const int n, const int m){F0R(i, n)F0R(j, m)cin>>v[i][j];}
ll binpow(ll a, ll b) {
ll res = 1;
while (b > 0) {
if (b & 1)
res = res * a;
a = a * a;
b >>= 1;
}
return res;
}
vi dista(10001), distb(10001);
vvi g(10001);
int a = 0, b = 0, d = 0, a1 = 0, a2 = 0, a3 = 0, a4 = 0, b1 = 0, b2 = 0, b3 = 0, b4 = 0;
void dfs(int u, int p, bool f){
trav(v, g[u]){
if(p == v)continue;
if(f)dista[v] = dista[u] + 1;
else distb[v] = distb[u] + 1;
dfs(v, u, f);
}
}
int send_message(int N, int i, int Pi){
g[i].pb(Pi);
g[Pi].pb(i);
dista[i] = dista[Pi] + 1;
distb[i] = distb[Pi] + 1;
//if(i == 21)_print(dista, distb);
if(distb[i] > d){
dista[i] = 0;
dfs(i, -1, 1);
d = distb[i];
if(i < N - 21)a = i;
else if(i < N - 9)a1 = i - (N - 21) + 1;
else if(i < N - 5)a2 = i - (N - 9) + 1;
else if(i < N - 2)a3 = i - (N - 5) + 1;
else a4 = i - (N - 2) + 1;
}
else if(dista[i] > d){
distb[i] = 0;
dfs(i, -1, 0);
d = dista[i];
if(i < N - 21)b = i;
else if(i < N - 9)b1 = i - (N - 21) + 1;
else if(i < N - 5)b2 = i - (N - 9) + 1;
else if(i < N - 1)b3 = i - (N - 5) + 1;
else b4 = 1;
}
//_print(a, a1, a2, a3, a4, b, b1, b2, b3, b4, d);
if(i < N - 21)return 0;
if(i < N - 15){
int x = a % 5;
a /= 5;
return x;
}
if(i < N - 9){
int x = b % 5;
b /= 5;
return x;
}
if(i < N - 7){
int x = a1 % 5;
a1 /= 5;
return x;
}
if(i < N - 5){
int x = b1 % 5;
b1 /= 5;
return x;
}
if(i < N - 4)return a2;
if(i < N - 3)return b2;
if(i < N - 2)return a3;
if(i < N - 1)return b3;
if(a4 == 1 && b4 == 1)return 1;
if(a4 == 1)return 2;
if(a4 == 2)return 3;
if(b4 == 1)return 4;
return 0;
}
std::pair<int,int> longest_path(std::vector<int> S){
int ca = 0, cb = 0, fa = 0, fb = 0;
int N = sz(S);
ROF(i, N - 21, N - 15){
ca *= 5;
ca += S[i];
}
ROF(i, N - 15, N - 9){
cb *= 5;
cb += S[i];
}
fa = ca;
ca = 0;
fb = cb;
cb = 0;
ROF(i, N - 9, N - 7){
ca *= 5;
ca += S[i];
}
ROF(i, N - 7, N - 5){
cb *= 5;
cb += S[i];
}
if(ca > 0)fa = ca + N - 21 - 1;
if(cb > 0)fb = cb + N - 21 - 1;
if(S[N - 5]){
fa = N - 9 - 1 + S[N - 5];
}
if(S[N - 4]){
fb = N - 9 - 1 + S[N - 4];
}
if(S[N - 3]){
fa = N - 5 - 1 + S[N - 3];
}
if(S[N - 2]){
fb = N - 5 - 1 + S[N - 2];
}
if(S[N - 1] == 1){
fa = N - 2;
fb = N - 1;
}
else if(S[N - 1] == 2){
fa = N - 2;
}
else if(S[N - 1] == 3){
fa = N - 1;
}
else if(S[N - 1] == 4){
fb = N - 1;
}
return mp(fa, fb);
}
/*
30
0 1 2 3 4 5 6 1 1 1 1 1 1 1 1 1 1 1 1 1 0 21 22 1 1 1 1 1 23
*/
