Jumping Path

#include <bits/stdc++.h>
using namespace std;

#define int long long

#define _ << " , " <<
#define bug(x) cout << #x << "  >>>>>>>  " << x << endl;
#define fastio ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);

#define ii pair<int, int>
#define fi first
#define se second

const int MAX = 1000100;
const int MOD = 11092019;
#define esq ((node << 1))
#define dir (((node << 1) | 1))
#define mid (((start + end) >> 1))

ii tree[4 * MAX];

ii merge(ii a, ii b) {
    ii c = { max(a.fi, b.fi), 0};
    if(c.fi == a.fi) c.se = (c.se + a.se) % MOD;
    if(c.fi == b.fi) c.se = (c.se + b.se) % MOD;
    return c;
}

ii query(int node, int start, int end, int l, int r) {
    if(l > end or r < start) return {-0x3f3f3f3f, 0};
    if(l <= start and end <= r) return tree[node];
    ii q1 = query(esq, start, mid, l, r);
    ii q2 = query(dir, mid + 1, end, l, r);
    return merge(q1, q2);
}

void update(int node, int start, int end, int idx, ii value) {
    if(start == end)
        tree[node] = value;
    else {
        if(start <= idx and idx <= mid) update(esq, start, mid, idx, value);
        else update(dir, mid + 1, end, idx, value);
        tree[node] = merge(tree[esq], tree[dir]);
    }
}

vector<int> G[MAX];
int label[MAX];

int lis(int v) {
    ii ant = query(1, 0, MAX - 1, label[v], label[v]);
    ii mx = query(1, 0, MAX - 1, 0, label[v]);
    update(1, 0, MAX - 1, label[v], ii(mx.fi + 1, mx.se));
    int l = tree[1].fi;
    for(int &u : G[v])
        l = max(l, lis(u));
    update(1, 0, MAX - 1, label[v], ant);
    return l;
}

int count(int v, int lis) {
    ii ant = query(1, 0, MAX - 1, label[v], label[v]);
    ii mx = query(1, 0, MAX - 1, 0, label[v]);
    int cnt = 0;
    bool undo_op = true;
    if(mx.fi + 1 == lis) {
        cnt = mx.se;
        mx = {-1, 0};
        undo_op = false;
    }
    update(1, 0, MAX - 1, label[v], ii(mx.fi + 1, mx.se));
    for(int &u : G[v])
        cnt = (cnt + count(u, lis)) % MOD;
    if(undo_op)
        update(1, 0, MAX - 1, label[v], ant);
    return cnt;
}

int32_t main() {
    fastio;

    int n;
    cin >> n;
    for(int i = 1; i <= n; ++i) cin >> label[i], label[i]++;

    for(int i = 2; i <= n; ++i) {
        int j;
        cin >> j;
        G[j].push_back(i);
    }

    update(1, 0, MAX - 1, 0, ii(0, 1));

    int l = lis(1);
    int cnt = count(1, l);

    cout << l << ' ' << cnt << '\n';

    return 0;
}