#include <bits/stdc++.h>
#define ll long long
#define pii pair<int, int>
using namespace std;
const int N = 1e5+1;
int tree[4*N];
void update(int idx, int l = 0, int r = N-1, int node=1) {
if (l == r) {
tree[node] = 1;
return;
}
const int mid = (l+r)/2;
if (idx <= mid)
update(idx, l, mid, node*2);
else
update(idx, mid+1, r, node*2+1);
tree[node] = tree[node*2] + tree[node*2+1];
}
int range_sum(int ql, int qr, int l = 0, int r = N-1, int node=1) {
if (ql <= l && r <= qr) return tree[node];
if (l > qr || r < ql) return 0;
const int mid = (l+r)/2;
return range_sum(ql, qr, l, mid, node*2) + range_sum(ql, qr, mid+1, r, node*2+1);
}
vector<int> adj[N];
int ttm, dt[N], ft[N];
void dfs(int node) {
dt[node] = ttm++;
for (int ch : adj[node]) {
dfs(ch);
}
ft[node] = ttm-1;
}
int ismad(int node) {
return range_sum(dt[node], ft[node]) < ft[node] - dt[node] + 1;
}
int solve(int n, int m, std::vector<int> P, std::vector<std::vector<int>> S) {
memset(tree, 0, sizeof tree);
ttm = 0;
for (int i = 0; i < n; i++) {
adj[i].clear();
}
for (int i = 1; i < n; i++) {
adj[P[i]].push_back(i);
}
dfs(0);
int days = 0;
int idx = 0;
int madcnt = 0;
while (idx < n-1) {
do {
for (int i = 0; i < m; i++) {
// append S[i][idx] if not appended
if (range_sum(dt[S[i][idx]], dt[S[i][idx]]) == 0) {
update(dt[S[i][idx]]);
int node = S[i][idx];
if (ismad(node)) {
madcnt++;
} else {
while (node != 0 && !ismad(P[node])) {
madcnt--;
node = P[node];
}
}
}
}
idx++;
}
while (idx < n-1 && (range_sum(0, n) != idx || madcnt));
days++;
}
return days;
}
#ifdef MUAATH_5
int main()
{
ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
cout << solve(3, 1, {-1, 0, 0}, {{1, 2}}) << '\n';
cout << solve(5, 2, {-1, 0, 0, 1, 1}, {{1, 2, 3, 4}, {4, 1, 2, 3}}) << '\n';
cout << solve(7, 1, {-1, 0, 0, 1, 1, 3, 3}, {{3, 1, 4, 6, 2}}) << '\n';
}
#endif
