#include "september.h"
#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 5;
const int LG = 20;
int in[N], out[N], sub[N], up[N][LG], st[N * 4], lzy[N * 4], st_[N * 4], lzy_[N * 4], cnt[N], max_p[N], tmr = 0, n, m;
vector<int> adj[N];
void dfs(int u, int p) {
sub[u] = 1;
in[u] = ++tmr;
up[u][0] = p;
for (int i = 1; i < LG; i++)
up[u][i] = up[up[u][i - 1]][i - 1];
for (auto v : adj[u]) {
if (v == p) continue;
dfs(v, u);
sub[u] += sub[v];
}
out[u] = tmr;
}
void relax(int v, int l, int r) {
if (lzy[v] == -1) return;
if (l != r) {
lzy[v * 2] = lzy[v];
lzy[v * 2 + 1] = lzy[v];
}
st[v] = (r - l + 1) * lzy[v];
lzy[v] = -1;
}
void upd(int v, int l, int r, int ul, int ur, int x) {
relax(v, l, r);
if (l > ur || r < ul) return;
if (l >= ul && r <= ur) {
lzy[v] = x;
relax(v, l, r);
return;
}
int mid = (l + r) >> 1;
upd(v * 2, l, mid, ul, ur, x);
upd(v * 2 + 1, mid + 1, r, ul, ur, x);
st[v] = st[v * 2] + st[v * 2 + 1];
}
int ask(int v, int l, int r, int ql, int qr) {
relax(v, l, r);
if (l > qr || r < ql) return 0;
if (l >= ql && r <= qr) return st[v];
int mid = (l + r) >> 1;
return ask(v * 2, l, mid, ql, qr) + ask(v * 2 + 1, mid + 1, r, ql, qr);
}
void relax_(int v, int l, int r) {
if (lzy_[v] == -1) return;
if (l != r) {
lzy_[v * 2] = lzy_[v];
lzy_[v * 2 + 1] = lzy_[v];
}
st_[v] = (r - l + 1) * lzy_[v];
lzy_[v] = -1;
}
void upd_(int v, int l, int r, int ul, int ur, int x) {
relax_(v, l, r);
if (l > ur || r < ul) return;
if (l >= ul && r <= ur) {
lzy_[v] = x;
relax_(v, l, r);
return;
}
int mid = (l + r) >> 1;
upd_(v * 2, l, mid, ul, ur, x);
upd_(v * 2 + 1, mid + 1, r, ul, ur, x);
st_[v] = st_[v * 2] + st_[v * 2 + 1];
}
int ask_(int v, int l, int r, int ql, int qr) {
relax_(v, l, r);
if (l > qr || r < ql) return 0;
if (l >= ql && r <= qr) return st_[v];
int mid = (l + r) >> 1;
return ask_(v * 2, l, mid, ql, qr) + ask_(v * 2 + 1, mid + 1, r, ql, qr);
}
int upper(int u) {
for (int i = LG - 1; i >= 0; i--) {
int v = up[u][i];
if (v != 0 && ask(1, 1, n, in[v], in[v]) > 0)
u = v;
}
return u;
}
void clear_all(int n_size) {
tmr = 0;
for (int i = 0; i <= n_size + 1; i++) {
adj[i].clear();
max_p[i] = 0;
for (int j = 0; j < LG; j++) up[i][j] = 0;
}
memset(st, 0, sizeof(int) * (n_size * 4 + 1));
memset(st_, 0, sizeof(int) * (n_size * 4 + 1));
memset(lzy, -1, sizeof(int) * (n_size * 4 + 1));
memset(lzy_, -1, sizeof(int) * (n_size * 4 + 1));
}
int solve(int n_, int m_, vector<int> F, vector<vector<int>> S) {
n = n_; m = m_;
clear_all(n);
for (int i = 1; i < n; i++) {
adj[F[i] + 1].push_back(i + 1);
}
for (int i = 0; i < m; i++) {
for (int j = 0; j < n - 1; j++) {
S[i][j]++;
max_p[S[i][j]] = max(max_p[S[i][j]], j);
}
}
dfs(1, 0);
int k = 0;
int cur_max_idx = 0;
for (int i = 0; i < n - 1; i++) {
int node = S[0][i];
cur_max_idx = max(cur_max_idx, max_p[node]);
bool ok = ask(1, 1, n, in[node], in[node]);
if (ok == false) {
cnt[node] = sub[node] - ask(1, 1, n, in[node], out[node]) - 1;
upd_(1, 1, n, in[node], out[node], 0);
upd_(1, 1, n, in[node], in[node], cnt[node]);
upd(1, 1, n, in[node], out[node], 1);
} else {
int up_node = upper(node);
cnt[up_node]--;
upd_(1, 1, n, in[up_node], in[up_node], cnt[up_node]);
}
if (ask_(1, 1, n, 1, n) == 0 && cur_max_idx == i) {
k++;
}
}
return k;
}
