#include "september.h"
#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 5;
const int LG = 20;
int n, tmr, inf[5];
int in[N], out[N], sub[N], up[N][LG];
int lzy[5][N * 4], lzy2[5][N * 4], st[5][N * 4], st2[5][N * 4], st3[5][N * 4];
vector < int > adj[N];
void dfs(int u, int p){
in[u] = ++tmr;
sub[u] = 1;
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]){
dfs(v, u);
sub[u] += sub[v];
}
out[u] = tmr;
}
void relax(int m, int v, int l, int r){
if(lzy[m][v] == -1)return;
if(l != r){
lzy[m][v * 2] = lzy[m][v];
lzy[m][v * 2 + 1] = lzy[m][v];
}
st2[m][v] = (r - l + 1) * lzy[m][v];
lzy[m][v] = -1;
}
void relax2(int m, int v, int l, int r){
if(lzy2[m][v] == -1)return;
if(l != r){
lzy2[m][v * 2] = lzy2[m][v];
lzy2[m][v * 2 + 1] = lzy2[m][v];
}
st3[m][v] = (r - l + 1) * lzy2[m][v];
lzy2[m][v] = -1;
}
void upd(int m, int v, int l, int r, int pos){
if(l == r){
st[m][v] = 1;
return;
}
int mid = (l + r) >> 1;
if(mid >= pos)upd(m, v * 2, l, mid, pos);
else upd(m, v * 2 + 1, mid + 1, r, pos);
st[m][v] = st[m][v * 2] + st[m][v * 2 + 1];
}
int ask(int m, int v, int l, int r, int ql, int qr){
if(l > qr || r < ql)return 0;
if(l >= ql && r <= qr)return st[m][v];
int mid = (l + r) >> 1;
return ask(m, v * 2, l, mid, ql, qr) + ask(m, v * 2 + 1, mid + 1, r, ql, qr);
}
void upd2(int m, int v, int l, int r, int ul, int ur, int x){
relax(m, v, l, r);
if(l > ur || r < ul)return;
if(l >= ul && r <= ur){
lzy[m][v] = x;
relax(m, v, l, r);
return;
}
int mid = (l + r) >> 1;
upd2(m, v * 2, l, mid, ul, ur, x);
upd2(m, v * 2 + 1, mid + 1, r, ul, ur, x);
st2[m][v] = st2[m][v * 2] + st2[m][v * 2 + 1];
}
int ask2(int m, int v, int l, int r, int ql, int qr){
relax(m, v, l, r);
if(l > qr || r < ql)return 0;
if(l >= ql && r <= qr)return st2[m][v];
int mid = (l + r) >> 1;
return ask2(m, v * 2, l, mid, ql, qr) + ask2(m, v * 2 + 1, mid + 1, r, ql, qr);
}
void upd3(int m, int v, int l, int r, int ul, int ur){
relax2(m, v, l, r);
if(l > ur || r < ul)return;
if(l >= ul && r <= ur){
lzy2[m][v] = 1;
relax2(m, v, l, r);
return;
}
int mid = (l + r) >> 1;
upd3(m, v * 2, l, mid, ul, ur);
upd3(m, v * 2 + 1, mid + 1, r, ul, ur);
st3[m][v] = st3[m][v * 2] + st3[m][v * 2 + 1];
}
int ask3(int m, int v, int l, int r, int ql, int qr){
relax2(m, v, l, r);
if(l > qr || r < ql)return 0;
if(l >= ql && r <= qr)return st3[m][v];
int mid = (l + r) >> 1;
return ask3(m, v * 2, l, mid, ql, qr) + ask3(m, v * 2 + 1, mid + 1, r, ql, qr);
}
bool ok(int node, int m){
int anc = -1;
int cur = up[node][0];
if(cur && ask3(m, 1, 1, n, in[cur], in[cur]) >= 1){
anc = cur;
for(int i = LG - 1; i >= 0; i--){
int nxt = up[anc][i];
if(nxt && ask3(m, 1, 1, n, in[nxt], in[nxt]) >= 1)anc = nxt;
}
}
if(anc == -1)return true;
int total = ask(m, 1, 1, n, in[anc], out[anc]);
if(sub[anc] == total){
inf[m] -= ask2(m, 1, 1, n, in[anc], out[anc]);
upd2(m, 1, 1, n, in[anc], out[anc], 0);
}
return (sub[anc] == total);
}
int solve(int n_, int m, vector<int> F, vector<vector<int>> S){
n = n_, tmr = 0;
for(int i = 0; i <= n; i++){
adj[i].clear();
in[i] = out[i] = sub[i] = 0;
for(int j = 0; j < LG; j++)
up[i][j] = 0;
}
for(int j = 0; j < m; j++){
inf[j] = 0;
for(int i = 0; i <= n * 4; i++){
lzy[j][i] = lzy2[j][i] = -1;
st[j][i] = st2[j][i] = st3[j][i] = 0;
}
}
for(int i = 1; i < n; i++)
adj[F[i] + 1].push_back(i + 1);
dfs(1, 1);
int k = 0;
for(int i = 0; i < n - 1; i++){
bool all = true;
for(int j = 0; j < m; j++){
int node = S[j][i] + 1;
upd3(j, 1, 1, n, in[node], out[node]);
upd(j, 1, 1, n, in[node]);
bool is1 = (ask(j, 1, 1, n, in[node], out[node]) == sub[node]);
bool is2 = ok(node, j);
if(!is1 || !is2){
upd2(j, 1, 1, n, in[node], in[node], 1);
inf[j]++;
}
all &= (is1 && is2 && inf[j] == 0);
}
if(all)k++;
}
return k;
}
/*
6 1
0 0 1 3 1
5 3 1 2 4
*/
