#include "circuit.h"
#include <bits/stdc++.h>
using namespace std;
#define sp " "
#define endl "\n"
#define pii pair<int, int>
#define st first
#define nd second
#define fileio() freopen("input.txt", "r", stdin), freopen("output.txt", "w", stdout)
#define fastio() cin.tie(0), ios_base::sync_with_stdio(0)
#define pb push_back
#define LL node * 2
#define RR node * 2 + 1
#define ll long long
#define MAXN 500005
const int modulo = 1000002022;
const ll INF = 2e18 + 7;
int add(ll a, ll b){
if (a + b < modulo) return a + b;
return a + b - modulo;
}
int subs(ll a, ll b){
if (a < b) return a - b + modulo;
return a - b;
}
int mul(ll a, ll b){
return (a * b) % modulo;
}
int fe(ll a, ll b){
if (b == 0) return 1;
if (b % 2) return mul(a, fe(a, b - 1));
int tmp = fe(a, b / 2);
return mul(tmp, tmp);
}
vector<int> adj[MAXN];
vector<int> dp[MAXN];
int one[MAXN], zero[MAXN], arr[MAXN];
int n, m;
void dfs(int node){
if (adj[node].empty()){
if (arr[node - n]) one[node] = 1;
else one[node] = 0;
zero[node] = 1 - one[node];
return;
}
int k = adj[node].size();
dp[node].resize(k + 1, 0);
fill(dp[node].begin(), dp[node].end(), 0);
dp[node][0] = 1;
for (auto i : adj[node]){
dfs(i);
for (int j = k; j >= 1; j--){
dp[node][j] = add(mul(dp[node][j], zero[i]), mul(dp[node][j - 1], one[i]));
}
dp[node][0] = mul(dp[node][0], zero[i]);
}
zero[node] = 0, one[node] = 0;
for (int i = 0; i <= k; i++){
zero[node] = add(zero[node], mul(dp[node][i], k - i));
one[node] = add(one[node], mul(dp[node][i], i));
}
}
void init(int N, int M, std::vector<int> P, std::vector<int> A) {
n = N, m = M;
for (int i = 1; i < n + m; i++)
adj[P[i]].pb(i);
for (int i = 0; i < m; i++) arr[i] = A[i];
}
int count_ways(int L, int R) {
for (int i = L - n; i <= R - n; i++)
arr[i] ^= 1;
dfs(0);
return one[0];
}
/*
int main() {
fileio();
int N, M, Q;
assert(3 == scanf("%d %d %d", &N, &M, &Q));
std::vector<int> P(N + M), A(M);
for (int i = 0; i < N + M; ++i) {
assert(1 == scanf("%d", &P[i]));
}
for (int j = 0; j < M; ++j) {
assert(1 == scanf("%d", &A[j]));
}
init(N, M, P, A);
for (int i = 0; i < Q; ++i) {
int L, R;
assert(2 == scanf("%d %d", &L, &R));
printf("%d\n", count_ways(L, R));
}
return 0;
}*/
