#include<bits/stdc++.h>
using namespace std;
#define pb push_back
int p[10001];
int send_message(int N, int i, int Pi) {
p[i] = Pi;
if (i == N-1) {
vector<vector<int>> graph(10001);
for (int i = N; i >= 1; i--)
graph[p[i]].pb(i);
vector<int> depth(10001, 0);
auto dfs = [&](auto &dfs, int u, int p, int dep = 0) -> void {
depth[u] = dep;
for (int e : graph[u])
if (e != p)
dfs(dfs, e, u, dep+1);
};
dfs(dfs, 0, 0);
int mx = 1;
for (int i = 2; i <= N; i++) {
if (depth[i] > depth[mx])
mx = i;
}
return max(0, mx-2);
}
return 0;
}
pair<int, int> longest_path(vector<int> S) {
return make_pair(0, min((int)S.size()-1, S.back()+2));
}
