Fu_L's Library

This documentation is automatically generated by online-judge-tools/verification-helper

View the Project on GitHub Fu-L/cp-library

:heavy_check_mark: verify/unit_test/tree/auxiliary_tree.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "../../../src/template/template.hpp"
#include "../../../src/random/random_number_generator.hpp"
#include "../../../src/template/static_modint.hpp"
using mint = modint998244353;
#include "../../../src/graph/graph_template.hpp"
#include "../../../src/tree/auxiliary_tree.hpp"
// ABC340-G
void test() {
    int n = rng(1, 500);
    int ma = rng(1, n);
    vector<int> a = rng.vec(n, 1, ma, true);
    auto [u, v] = rng.tree(n, true);
    auto brute = [&](int n, vector<int> a, vector<int> u, vector<int> v) -> mint {
        rep(i, 0, n) {
            a[i]--;
        }
        Graph<int> g(n);
        rep(i, 0, n - 1) {
            u[i]--;
            v[i]--;
            g.add_edge(u[i], v[i]);
        }
        mint ans = 0;
        rep(i, 0, n) {
            map<int, mint> dp1, dp2;
            auto dfs = [&](auto& dfs, int cur, int p) -> void {
                dp1[cur] = 1;
                dp2[cur] = 1;
                for(const auto& e : g[cur]) {
                    if(e.to == p) continue;
                    dfs(dfs, e.to, cur);
                    dp1[cur] *= dp2[e.to] + 1;
                    dp2[cur] *= dp2[e.to] + 1;
                }
                if(a[cur] != i) {
                    for(const auto& e : g[cur]) {
                        if(e.to == p) continue;
                        dp1[cur] -= dp2[e.to];
                    }
                    dp1[cur]--;
                    dp2[cur]--;
                }
                ans += dp1[cur];
            };
            dfs(dfs, 0, -1);
        }
        return ans;
    };
    auto fast = [&](int n, vector<int> a, vector<int> u, vector<int> v) -> mint {
        vector<vector<int>> col(n);
        rep(i, 0, n) {
            a[i]--;
            col[a[i]].push_back(i);
        }
        Graph<int> g(n);
        rep(i, 0, n - 1) {
            u[i]--;
            v[i]--;
            g.add_edge(u[i], v[i]);
        }
        AuxiliaryTree<int> aux(g);
        mint ans = 0;
        rep(i, 0, n) {
            if(col[i].empty()) continue;
            auto [tree, idx] = aux.get(col[i]);
            map<int, mint> dp1, dp2;
            auto dfs = [&](auto& dfs, int cur, int p) -> void {
                dp1[cur] = 1;
                dp2[cur] = 1;
                for(const auto& e : tree[cur]) {
                    if(e.to == p) continue;
                    dfs(dfs, e.to, cur);
                    dp1[cur] *= dp2[e.to] + 1;
                    dp2[cur] *= dp2[e.to] + 1;
                }
                if(a[idx[cur]] != i) {
                    for(const auto& e : tree[cur]) {
                        if(e.to == p) continue;
                        dp1[cur] -= dp2[e.to];
                    }
                    dp1[cur]--;
                    dp2[cur]--;
                }
                ans += dp1[cur];
            };
            dfs(dfs, 0, -1);
        }
        return ans;
    };
    assert(brute(n, a, u, v) == fast(n, a, u, v));
}
int main(void) {
    constexpr int test_num = 100;
    rep(i, 0, test_num) {
        test();
    }
    int a, b;
    cin >> a >> b;
    cout << a + b << '\n';
}
#line 1 "verify/unit_test/tree/auxiliary_tree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/random/random_number_generator.hpp"
struct RandomNumberGenerator {
    RandomNumberGenerator()
        : mt(chrono::steady_clock::now().time_since_epoch().count()) {}
    template <typename T>
    inline T operator()(const T lower, const T upper) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(lower <= upper);
        if constexpr(is_integral_v<T>) {
            uniform_int_distribution<T> dist(lower, upper);
            return dist(mt);
        } else if constexpr(is_floating_point_v<T>) {
            uniform_real_distribution<T> dist(lower, upper);
            return dist(mt);
        }
    }
    template <typename T>
    inline vector<T> vec(const int n, const T lower, const T upper, const bool dup = true) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(0 <= n and n <= (int)1e8);
        assert(lower <= upper);
        if(n == 0) return {};
        vector<T> res(n);
        if(dup or is_floating_point_v<T>) {
            for(int i = 0; i < n; ++i) res[i] = this->operator()(lower, upper);
        } else {
            assert(upper - lower + 1 >= n);
            if(upper - lower + 1 >= 2 * n) {
                set<T> used;
                while((int)used.size() < n) {
                    const T a = this->operator()(lower, upper);
                    used.insert(a);
                }
                int i = 0;
                for(const T a : used) {
                    res[i] = a;
                    ++i;
                }
            } else {
                const vector<int> p = perm(upper - lower + 1, false);
                for(int i = 0; i < n; ++i) {
                    res[i] = p[i] + lower;
                }
            }
        }
        return res;
    }
    inline vector<int> perm(const int n, const bool one = true) {
        assert(0 <= n and n <= (int)1e8);
        vector<int> res(n);
        for(int i = 0; i < n; ++i) res[i] = i + one;
        for(int i = n - 1; i > 0; --i) {
            swap(res[i], res[this->operator()(0, i)]);
        }
        return res;
    }
    inline pair<vector<int>, vector<int>> tree(const int n, const bool one = true) {
        assert(0 <= n and n <= (int)1e8);
        if(n <= 1) return {{}, {}};
        if(n == 2) return {{0 + one}, {1 + one}};
        vector<int> u(n - 1), v(n - 1);
        const vector<int> pruefer = vec(n - 2, 0, n - 1);
        set<int> st;
        vector<int> cnt(n);
        for(int i = 0; i < n; ++i) st.insert(i);
        auto add = [&](const int x) -> void {
            if(x > n) return;
            if(cnt[x] == 0) st.erase(x);
            ++cnt[x];
        };
        auto del = [&](const int x) -> void {
            if(x > n) return;
            --cnt[x];
            if(cnt[x] == 0) st.insert(x);
        };
        for(int i = 0; i < n - 2; ++i) add(pruefer[i]);
        for(int i = 0; i < n - 2; ++i) {
            const int a = *st.begin();
            const int b = pruefer[i];
            u[i] = a + one;
            v[i] = b + one;
            del(b);
            add(a);
        }
        const int a = *st.begin();
        add(a);
        const int b = *st.begin();
        u[n - 2] = a + one;
        v[n - 2] = b + one;
        return {u, v};
    }
    template <typename T>
    inline tuple<vector<int>, vector<int>, vector<T>> weighted_tree(const int n, const T lower, const T upper, const bool one = true) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(0 <= n and n <= (int)1e8);
        assert(lower <= upper);
        if(n == 0) return {{}, {}, {}};
        const auto [u, v] = tree(n, one);
        const vector<T> w = vec(n - 1, lower, upper, true);
        return {u, v, w};
    }
    inline pair<vector<int>, vector<int>> graph(const int n, const int m, const bool one = true) {
        assert(0 <= n and n <= (int)1e8);
        assert(0 <= m and m <= (int)min((ll)1e8, 1ll * n * (n - 1) / 2));
        vector<int> u, v;
        u.reserve(m);
        v.reserve(m);
        if(1ll * n * (n - 1) / 2 >= 2e6) {
            set<pair<int, int>> edge;
            while((int)edge.size() < m) {
                const int a = this->operator()(0, n - 1);
                const int b = this->operator()(0, n - 1);
                if(a >= b) continue;
                edge.insert({a, b});
            }
            for(const auto& [a, b] : edge) {
                u.push_back(a + one);
                v.push_back(b + one);
            }
        } else {
            vector<pair<int, int>> edge;
            edge.reserve(n * (n - 1) / 2);
            for(int i = 0; i < n; ++i) {
                for(int j = i + 1; j < n; ++j) {
                    edge.push_back({i, j});
                }
            }
            const vector<int> p = perm(n * (n - 1) / 2, false);
            for(int i = 0; i < m; ++i) {
                u.push_back(edge[p[i]].first + one);
                v.push_back(edge[p[i]].second + one);
            }
        }
        return {u, v};
    }
    template <typename T>
    inline tuple<vector<int>, vector<int>, vector<T>> weighted_graph(const int n, const int m, const T lower, const T upper, const bool one = true) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(0 <= n and n <= (int)1e8);
        assert(0 <= m and m <= (int)min((ll)1e8, 1ll * n * (n - 1) / 2));
        assert(lower <= upper);
        const auto [u, v] = graph(n, m, one);
        const vector<T> w = vec(m, lower, upper, true);
        return {u, v, w};
    }
    inline pair<vector<int>, vector<int>> connected_graph(const int n, const int m, const bool one = true) {
        assert(0 <= n and n <= (int)1e8);
        assert(max(n - 1, 0) <= m and m <= (int)min((ll)1e8, 1ll * n * (n - 1) / 2));
        if(n <= 1) return {{}, {}};
        vector<int> u, v;
        u.reserve(m);
        v.reserve(m);
        auto [ut, vt] = tree(n, false);
        if(1ll * n * (n - 1) / 2 >= 2e6) {
            set<pair<int, int>> edge;
            for(int i = 0; i < n - 1; ++i) {
                edge.insert({min(ut[i], vt[i]), max(ut[i], vt[i])});
            }
            while((int)edge.size() < m) {
                const int a = this->operator()(0, n - 1);
                const int b = this->operator()(0, n - 1);
                if(a >= b) continue;
                edge.insert({a, b});
            }
            for(const auto& [a, b] : edge) {
                u.push_back(a + one);
                v.push_back(b + one);
            }
        } else {
            set<pair<int, int>> used;
            for(int i = 0; i < n - 1; ++i) {
                u.push_back(ut[i] + one);
                v.push_back(vt[i] + one);
                used.insert({min(ut[i], vt[i]), max(ut[i], vt[i])});
            }
            vector<pair<int, int>> edge;
            edge.reserve(n * (n - 1) / 2 - (n - 1));
            for(int i = 0; i < n; ++i) {
                for(int j = i + 1; j < n; ++j) {
                    if(used.find({i, j}) == used.end()) edge.push_back({i, j});
                }
            }
            const vector<int> p = perm(n * (n - 1) / 2 - (n - 1), false);
            for(int i = 0; i < m - (n - 1); ++i) {
                u.push_back(edge[p[i]].first + one);
                v.push_back(edge[p[i]].second + one);
            }
        }
        return {u, v};
    }
    template <typename T>
    inline tuple<vector<int>, vector<int>, vector<T>> weighted_connected_graph(const int n, const int m, const T lower, const T upper, const bool one = true) {
        static_assert(is_integral_v<T> or is_floating_point_v<T>);
        assert(0 <= n and n <= (int)1e8);
        assert(max(n - 1, 0) <= m and m <= (int)min((ll)1e8, 1ll * n * (n - 1) / 2));
        assert(lower <= upper);
        const auto [u, v] = connected_graph(n, m, one);
        const vector<T> w = vec(m, lower, upper, true);
        return {u, v, w};
    }
    inline string parenthesis(const int n) {
        assert(0 <= n and n <= 1e8);
        string res = "";
        int N = n, M = n;
        for(int i = 0; i < 2 * n; ++i) {
            if(this->operator()(0.0l, 1.0l) > 1.0l * (N - M) * (N + 1) / ((N - M + 1) * (N + M))) {
                res += "(";
                --M;
            } else {
                res += ")";
                --N;
            }
        }
        return res;
    }

   private:
    mt19937_64 mt;
} rng;
#line 3 "src/template/static_modint.hpp"
template <uint32_t m>
struct StaticModint {
    using mint = StaticModint;
    static constexpr uint32_t mod() {
        return m;
    }
    static constexpr mint raw(const uint32_t v) {
        mint a;
        a._v = v;
        return a;
    }
    constexpr StaticModint()
        : _v(0) {}
    template <class T>
    constexpr StaticModint(const T& v) {
        static_assert(is_integral_v<T>);
        if constexpr(is_signed_v<T>) {
            int64_t x = int64_t(v % int64_t(m));
            if(x < 0) x += m;
            _v = uint32_t(x);
        } else _v = uint32_t(v % m);
    }
    constexpr uint32_t val() const {
        return _v;
    }
    constexpr mint& operator++() {
        return *this += 1;
    }
    constexpr mint& operator--() {
        return *this -= 1;
    }
    constexpr mint operator++(int) {
        mint res = *this;
        ++*this;
        return res;
    }
    constexpr mint operator--(int) {
        mint res = *this;
        --*this;
        return res;
    }
    constexpr mint& operator+=(mint rhs) {
        if(_v >= m - rhs._v) _v -= m;
        _v += rhs._v;
        return *this;
    }
    constexpr mint& operator-=(mint rhs) {
        if(_v < rhs._v) _v += m;
        _v -= rhs._v;
        return *this;
    }
    constexpr mint& operator*=(mint rhs) {
        return *this = *this * rhs;
    }
    constexpr mint& operator/=(mint rhs) {
        return *this *= rhs.inv();
    }
    constexpr mint operator+() const {
        return *this;
    }
    constexpr mint operator-() const {
        return mint{} - *this;
    }
    constexpr mint pow(long long n) const {
        assert(0 <= n);
        if(n == 0) return 1;
        mint x = *this, r = 1;
        while(1) {
            if(n & 1) r *= x;
            n >>= 1;
            if(n == 0) return r;
            x *= x;
        }
    }
    constexpr mint inv() const {
        if constexpr(prime) {
            assert(_v);
            return pow(m - 2);
        } else {
            const auto eg = inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend constexpr mint operator+(mint lhs, mint rhs) {
        return lhs += rhs;
    }
    friend constexpr mint operator-(mint lhs, mint rhs) {
        return lhs -= rhs;
    }
    friend constexpr mint operator*(mint lhs, mint rhs) {
        return uint64_t(lhs._v) * rhs._v;
    }
    friend constexpr mint operator/(mint lhs, mint rhs) {
        return lhs /= rhs;
    }
    friend constexpr bool operator==(mint lhs, mint rhs) {
        return lhs._v == rhs._v;
    }
    friend constexpr bool operator!=(mint lhs, mint rhs) {
        return lhs._v != rhs._v;
    }
    friend istream& operator>>(istream& in, mint& x) {
        long long a;
        in >> a;
        x = a;
        return in;
    }
    friend ostream& operator<<(ostream& out, const mint& x) {
        return out << x.val();
    }

   private:
    uint32_t _v = 0;
    static constexpr bool prime = []() -> bool {
        if(m == 1) return 0;
        if(m == 2 or m == 7 or m == 61) return 1;
        if(m % 2 == 0) return 0;
        uint32_t d = m - 1;
        while(d % 2 == 0) d /= 2;
        for(uint32_t a : {2, 7, 61}) {
            uint32_t t = d;
            mint y = mint(a).pow(t);
            while(t != m - 1 && y != 1 && y != m - 1) {
                y *= y;
                t <<= 1;
            }
            if(y != m - 1 && t % 2 == 0) return 0;
        }
        return 1;
    }();
    static constexpr pair<int32_t, int32_t> inv_gcd(const int32_t a, const int32_t b) {
        if(a == 0) return {b, 0};
        int32_t s = b, t = a, m0 = 0, m1 = 1;
        while(t) {
            const int32_t u = s / t;
            s -= t * u;
            m0 -= m1 * u;
            swap(s, t);
            swap(m0, m1);
        }
        if(m0 < 0) m0 += b / s;
        return {s, m0};
    }
};
using modint998244353 = StaticModint<998244353>;
using modint1000000007 = StaticModint<1000000007>;
#line 5 "verify/unit_test/tree/auxiliary_tree.test.cpp"
using mint = modint998244353;
#line 3 "src/graph/graph_template.hpp"
template <typename T>
struct Edge {
    int from, to;
    T cost;
    int idx;
    Edge()
        : from(-1), to(-1), cost(-1), idx(-1) {}
    Edge(const int from, const int to, const T& cost = 1, const int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}
    operator int() const {
        return to;
    }
};
template <typename T>
struct Graph {
    Graph(const int N)
        : n(N), es(0), g(N) {}
    int size() const {
        return n;
    }
    int edge_size() const {
        return es;
    }
    void add_edge(const int from, const int to, const T& cost = 1) {
        assert(0 <= from and from < n);
        assert(0 <= to and to < n);
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }
    void add_directed_edge(const int from, const int to, const T& cost = 1) {
        assert(0 <= from and from < n);
        assert(0 <= to and to < n);
        g[from].emplace_back(from, to, cost, es++);
    }
    inline vector<Edge<T>>& operator[](const int& k) {
        assert(0 <= k and k < n);
        return g[k];
    }
    inline const vector<Edge<T>>& operator[](const int& k) const {
        assert(0 <= k and k < n);
        return g[k];
    }

   private:
    int n, es;
    vector<vector<Edge<T>>> g;
};
template <typename T>
using Edges = vector<Edge<T>>;
#line 4 "src/tree/heavy_light_decomposition.hpp"
template <typename T>
struct HeavyLightDecomposition {
    HeavyLightDecomposition(Graph<T>& _g, const int root = 0)
        : g(_g), n(g.size()), id(0), sz(n, 0), dep(n, 0), down(n, -1), up(n, -1), nex(n, root), par(n, -1), rev(n, 0), co(n, 0) {
        assert(0 <= root and root < n);
        dfs_sz(root);
        dfs_hld(root);
    }
    pair<int, int> idx(const int i) const {
        assert(0 <= i and i < n);
        return make_pair(down[i], up[i]);
    }
    int depth(const int v) const {
        assert(0 <= v and v < n);
        return dep[v];
    }
    T cost(const int v) const {
        assert(0 <= v and v < n);
        return co[v];
    }
    int parent(const int v) const {
        assert(0 <= v and v < n);
        return par[v];
    }
    int la(int v, int x) const {
        assert(0 <= v and v < n);
        assert(x >= 0);
        if(x > dep[v]) return -1;
        while(true) {
            const int u = nex[v];
            if(down[v] - x >= down[u]) return rev[down[v] - x];
            x -= down[v] - down[u] + 1;
            v = par[u];
        }
    }
    int lca(int u, int v) const {
        assert(0 <= u and u < n);
        assert(0 <= v and v < n);
        while(nex[u] != nex[v]) {
            if(down[u] < down[v]) swap(u, v);
            u = par[nex[u]];
        }
        return dep[u] < dep[v] ? u : v;
    }
    int dist(const int u, const int v) const {
        assert(0 <= u and u < n);
        assert(0 <= v and v < n);
        return dep[u] + dep[v] - dep[lca(u, v)] * 2;
    }
    T length(const int u, const int v) const {
        assert(0 <= u and u < n);
        assert(0 <= v and v < n);
        return co[u] + co[v] - co[lca(u, v)] * 2;
    }
    template <typename F>
    void path_query(const int u, const int v, const bool vertex, const F& f) {
        assert(0 <= u and u < n);
        assert(0 <= v and v < n);
        const int l = lca(u, v);
        for(auto&& [a, b] : ascend(u, l)) f(a + 1, b);
        if(vertex) f(down[l], down[l] + 1);
        for(auto&& [a, b] : descend(l, v)) f(a, b + 1);
    }
    template <typename F>
    void subtree_query(const int v, const bool vertex, const F& f) {
        assert(0 <= v and v < n);
        f(down[v] + int(!vertex), up[v]);
    }

   private:
    Graph<T>& g;
    int n, id;
    vector<int> sz, dep, down, up, nex, par, rev;
    vector<T> co;
    void dfs_sz(const int cur) {
        sz[cur] = 1;
        for(Edge<T>& edge : g[cur]) {
            if(edge.to == par[cur]) {
                if(g[cur].size() >= 2 and edge.to == g[cur][0].to) {
                    swap(g[cur][0], g[cur][1]);
                } else {
                    continue;
                }
            }
            dep[edge.to] = dep[cur] + 1;
            co[edge.to] = co[cur] + edge.cost;
            par[edge.to] = cur;
            dfs_sz(edge.to);
            sz[cur] += sz[edge.to];
            if(sz[edge.to] > sz[g[cur][0].to]) {
                swap(edge, g[cur][0]);
            }
        }
    }
    void dfs_hld(const int cur) {
        down[cur] = id++;
        rev[down[cur]] = cur;
        for(const Edge<T>& edge : g[cur]) {
            if(edge.to == par[cur]) continue;
            nex[edge.to] = (edge.to == g[cur][0].to ? nex[cur] : edge.to);
            dfs_hld(edge.to);
        }
        up[cur] = id;
    }
    vector<pair<int, int>> ascend(int u, int v) const {
        vector<pair<int, int>> res;
        while(nex[u] != nex[v]) {
            res.emplace_back(down[u], down[nex[u]]);
            u = par[nex[u]];
        }
        if(u != v) res.emplace_back(down[u], down[v] + 1);
        return res;
    }
    vector<pair<int, int>> descend(const int u, const int v) const {
        if(u == v) return {};
        if(nex[u] == nex[v]) return {{down[u] + 1, down[v]}};
        auto res = descend(u, par[nex[v]]);
        res.emplace_back(down[nex[v]], down[v]);
        return res;
    }
};
#line 5 "src/tree/auxiliary_tree.hpp"
template <typename T>
struct AuxiliaryTree {
    AuxiliaryTree(const Graph<T>& _g, const int root = 0)
        : g(_g), hld(g, root) {}
    pair<Graph<int>, vector<int>> get(vector<int> idx) {
        if(idx.empty()) return {Graph<int>(0), {}};
        auto comp = [&](const int i, const int j) {
            return hld.idx(i).first < hld.idx(j).first;
        };
        sort(begin(idx), end(idx), comp);
        for(int i = 0, ie = idx.size(); i + 1 < ie; ++i) {
            idx.push_back(hld.lca(idx[i], idx[i + 1]));
        }
        sort(begin(idx), end(idx), comp);
        idx.erase(unique(begin(idx), end(idx)), end(idx));
        Graph<int> aux(idx.size());
        vector<int> rs;
        rs.push_back(0);
        for(int i = 1; i < (int)idx.size(); ++i) {
            const int l = hld.lca(idx[rs.back()], idx[i]);
            while(idx[rs.back()] != l) rs.pop_back();
            aux.add_directed_edge(rs.back(), i);
            rs.push_back(i);
        }
        return make_pair(aux, idx);
    }

   private:
    Graph<T> g;
    HeavyLightDecomposition<T> hld;
};
#line 8 "verify/unit_test/tree/auxiliary_tree.test.cpp"
// ABC340-G
void test() {
    int n = rng(1, 500);
    int ma = rng(1, n);
    vector<int> a = rng.vec(n, 1, ma, true);
    auto [u, v] = rng.tree(n, true);
    auto brute = [&](int n, vector<int> a, vector<int> u, vector<int> v) -> mint {
        rep(i, 0, n) {
            a[i]--;
        }
        Graph<int> g(n);
        rep(i, 0, n - 1) {
            u[i]--;
            v[i]--;
            g.add_edge(u[i], v[i]);
        }
        mint ans = 0;
        rep(i, 0, n) {
            map<int, mint> dp1, dp2;
            auto dfs = [&](auto& dfs, int cur, int p) -> void {
                dp1[cur] = 1;
                dp2[cur] = 1;
                for(const auto& e : g[cur]) {
                    if(e.to == p) continue;
                    dfs(dfs, e.to, cur);
                    dp1[cur] *= dp2[e.to] + 1;
                    dp2[cur] *= dp2[e.to] + 1;
                }
                if(a[cur] != i) {
                    for(const auto& e : g[cur]) {
                        if(e.to == p) continue;
                        dp1[cur] -= dp2[e.to];
                    }
                    dp1[cur]--;
                    dp2[cur]--;
                }
                ans += dp1[cur];
            };
            dfs(dfs, 0, -1);
        }
        return ans;
    };
    auto fast = [&](int n, vector<int> a, vector<int> u, vector<int> v) -> mint {
        vector<vector<int>> col(n);
        rep(i, 0, n) {
            a[i]--;
            col[a[i]].push_back(i);
        }
        Graph<int> g(n);
        rep(i, 0, n - 1) {
            u[i]--;
            v[i]--;
            g.add_edge(u[i], v[i]);
        }
        AuxiliaryTree<int> aux(g);
        mint ans = 0;
        rep(i, 0, n) {
            if(col[i].empty()) continue;
            auto [tree, idx] = aux.get(col[i]);
            map<int, mint> dp1, dp2;
            auto dfs = [&](auto& dfs, int cur, int p) -> void {
                dp1[cur] = 1;
                dp2[cur] = 1;
                for(const auto& e : tree[cur]) {
                    if(e.to == p) continue;
                    dfs(dfs, e.to, cur);
                    dp1[cur] *= dp2[e.to] + 1;
                    dp2[cur] *= dp2[e.to] + 1;
                }
                if(a[idx[cur]] != i) {
                    for(const auto& e : tree[cur]) {
                        if(e.to == p) continue;
                        dp1[cur] -= dp2[e.to];
                    }
                    dp1[cur]--;
                    dp2[cur]--;
                }
                ans += dp1[cur];
            };
            dfs(dfs, 0, -1);
        }
        return ans;
    };
    assert(brute(n, a, u, v) == fast(n, a, u, v));
}
int main(void) {
    constexpr int test_num = 100;
    rep(i, 0, test_num) {
        test();
    }
    int a, b;
    cin >> a >> b;
    cout << a + b << '\n';
}
Back to top page