#1101674 (C++23) No.3194 Do Optimize Your Solution

• 問題: No.3194 Do Optimize Your Solution
• ユーザー: akakimidori
• 提出日時: 2025-06-27 22:56:32
• 言語: C++23 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 2,515 ms / 3,000 ms
• コード長: 29,390 bytes
• コンパイル時間: 2,543 ms
• コンパイル使用メモリ: 153,808 KB
• 実行使用メモリ: 97,432 KB
• 最終ジャッジ日時: 2025-06-27 22:57:08
• 合計ジャッジ時間: 24,750 ms
• ジャッジサーバーID （参考情報）: judge1 / judge4

ファイルパターン	結果
sample	AC * 2
other	AC * 17

ソースコード

// https://judge.yosupo.jp/submission/207115
// を書き換え

#define PROBLEM "https://judge.yosupo.jp/problem/point_set_tree_path_composite_sum_fixed_root"
#include <vector>
#include <queue>
#include <utility>
#include <algorithm>
#include <memory>
#include <cassert>
#include <array>

namespace nachia{

template<class Elem>
class CsrArray{
public:
    struct ListRange{
        using iterator = typename std::vector<Elem>::iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        Elem& operator[](int i) const { return begi[i]; }
    };
    struct ConstListRange{
        using iterator = typename std::vector<Elem>::const_iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        const Elem& operator[](int i) const { return begi[i]; }
    };
private:
    int m_n;
    std::vector<Elem> m_list;
    std::vector<int> m_pos;
public:
    CsrArray() : m_n(0), m_list(), m_pos() {}
    static CsrArray Construct(int n, std::vector<std::pair<int, Elem>> items){
        CsrArray res;
        res.m_n = n;
        std::vector<int> buf(n+1, 0);
        for(auto& [u,v] : items){ ++buf[u]; }
        for(int i=1; i<=n; i++) buf[i] += buf[i-1];
        res.m_list.resize(buf[n]);
        for(int i=(int)items.size()-1; i>=0; i--){
            res.m_list[--buf[items[i].first]] = std::move(items[i].second);
        }
        res.m_pos = std::move(buf);
        return res;
    }
    static CsrArray FromRaw(std::vector<Elem> list, std::vector<int> pos){
        CsrArray res;
        res.m_n = pos.size() - 1;
        res.m_list = std::move(list);
        res.m_pos = std::move(pos);
        return res;
    }
    ListRange operator[](int u) { return ListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    ConstListRange operator[](int u) const { return ConstListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    int size() const { return m_n; }
    int fullSize() const { return (int)m_list.size(); }
};

} // namespace nachia

namespace nachia{


struct Graph {
public:
    struct Edge{
        int from, to;
        void reverse(){ std::swap(from, to); }
        int xorval() const { return from ^ to; }
    };
    Graph(int n = 0, bool undirected = false, int m = 0) : m_n(n), m_e(m), m_isUndir(undirected) {}
    Graph(int n, const std::vector<std::pair<int, int>>& edges, bool undirected = false) : m_n(n), m_isUndir(undirected){
        m_e.resize(edges.size());
        for(std::size_t i=0; i<edges.size(); i++) m_e[i] = { edges[i].first, edges[i].second };
    }
    template<class Cin>
    static Graph Input(Cin& cin, int n, bool undirected, int m, bool offset = 0){
        Graph res(n, undirected, m);
        for(int i=0; i<m; i++){
            int u, v; cin >> u >> v;
            res[i].from = u - offset;
            res[i].to = v - offset;
        }
        return res;
    }
    int numVertices() const noexcept { return m_n; }
    int numEdges() const noexcept { return int(m_e.size()); }
    int addNode() noexcept { return m_n++; }
    int addEdge(int from, int to){ m_e.push_back({ from, to }); return numEdges() - 1; }
    Edge& operator[](int ei) noexcept { return m_e[ei]; }
    const Edge& operator[](int ei) const noexcept { return m_e[ei]; }
    Edge& at(int ei) { return m_e.at(ei); }
    const Edge& at(int ei) const { return m_e.at(ei); }
    auto begin(){ return m_e.begin(); }
    auto end(){ return m_e.end(); }
    auto begin() const { return m_e.begin(); }
    auto end() const { return m_e.end(); }
    bool isUndirected() const noexcept { return m_isUndir; }
    void reverseEdges() noexcept { for(auto& e : m_e) e.reverse(); }
    void contract(int newV, const std::vector<int>& mapping){
        assert(numVertices() == int(mapping.size()));
        for(int i=0; i<numVertices(); i++) assert(0 <= mapping[i] && mapping[i] < newV);
        for(auto& e : m_e){ e.from = mapping[e.from]; e.to = mapping[e.to]; }
        m_n = newV;
    }
    std::vector<Graph> induce(int num, const std::vector<int>& mapping) const {
        int n = numVertices();
        assert(n == int(mapping.size()));
        for(int i=0; i<n; i++) assert(-1 <= mapping[i] && mapping[i] < num);
        std::vector<int> indexV(n), newV(num);
        for(int i=0; i<n; i++) if(mapping[i] >= 0) indexV[i] = newV[mapping[i]]++;
        std::vector<Graph> res; res.reserve(num);
        for(int i=0; i<num; i++) res.emplace_back(newV[i], isUndirected());
        for(auto e : m_e) if(mapping[e.from] == mapping[e.to] && mapping[e.to] >= 0) res[mapping[e.to]].addEdge(indexV[e.from], indexV[e.to]);
        return res;
    }
    CsrArray<int> getEdgeIndexArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(int i=0; i<numEdges(); i++){
            auto e = operator[](i);
            src.emplace_back(e.from, i);
            if(undirected) src.emplace_back(e.to, i);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getEdgeIndexArray() const { return getEdgeIndexArray(isUndirected()); }
    CsrArray<int> getAdjacencyArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(auto e : m_e){
            src.emplace_back(e.from, e.to);
            if(undirected) src.emplace_back(e.to, e.from);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getAdjacencyArray() const { return getAdjacencyArray(isUndirected()); }
private:
    int m_n;
    std::vector<Edge> m_e;
    bool m_isUndir;
};

} // namespace nachia

namespace nachia {

struct StaticTopTree {

    static const int TYPE_RAKE = 0;
    static const int TYPE_DANGLE = 1;
    static const int TYPE_COMPRESS = 2;
    static const int TYPE_SHUTOUT = 3;
    static const int TYPE_GAIN = 4;

    struct Node {
        int type;
        int arg1;
        int arg2;
        int arg3;
        int parent;
    };

    std::vector<int> ordered;
    std::vector<Node> nodes;
    std::vector<int> handle_v;
    std::vector<int> handle_e;
    Graph dtree;

    StaticTopTree() {}

    StaticTopTree(const Graph& tree, int root){
        int n = tree.numVertices();
        auto adj = tree.getAdjacencyArray();
        std::vector<int> parent(n, -1);
        std::vector<int> parentEdge(n, -1);
        std::vector<int> bfs(n);
        std::vector<int> sz(n, 1);
        std::vector<int> nx(n, -1);
        int z = 1; while((1<<z) < n) z++;
        handle_v.resize(n,-1);
        handle_e.resize(n-1,-1);
        int bfsi = 0;
        bfs[bfsi++] = root;
        for(int i=0; i<bfsi; i++){
            int v = bfs[i];
            for(int w : adj[v]) if(parent[v] != w){
                parent[w] = v; bfs[bfsi++] = w;
            }
        }
        dtree = Graph(n, false, n-1);
        for(int e=0; e<n-1; e++){
            auto [v,w] = tree[e];
            if(parent[w] != v) std::swap(v, w);
            dtree[e].from = v;
            dtree[e].to = w;
            parentEdge[w] = e;
        }
        for(int i=n-1; i>=0; i--){
            int v = bfs[i];
            if(i) sz[parent[v]] += sz[v];
            for(int w : adj[v]) if(w != parent[v]){
                if(nx[v] == -1 || sz[nx[v]] < sz[w]) nx[v] = w;
            }
        }
        auto pushGain = [&](int v) -> int {
            nodes.push_back({ TYPE_GAIN,v,-2,-3,-1 });
            return int(nodes.size()) - 1;
        };
        auto pushNode1 = [&](int a, int b, int c, int d) -> int {
            int res = int(nodes.size());
            nodes[b].parent = res;
            nodes.push_back({ a,b,c,d,-1 });
            return res;
        };
        auto pushNode2 = [&](int a, int b, int c, int d) -> int {
            int res = int(nodes.size());
            nodes[b].parent = nodes[c].parent = res;
            nodes.push_back({ a,b,c,d,-1 });
            return res;
        };
        auto dfs_c_x = [&](auto& dfs_c, auto& dfs_h, int v) -> std::pair<int,int> {
            std::priority_queue<std::pair<int,int>> que;
            ordered.push_back(v);
            for(int w : adj[v]) if(w != parent[v] && w != nx[v]){
                auto [h,s] = dfs_h(dfs_c, dfs_h, w);
                int e = parentEdge[w];
                handle_e[e] = pushNode1(TYPE_DANGLE, s, e, w);
                que.push({ -(h+1), handle_e[e] });
            }
            if(que.empty()){
                handle_v[v] = pushGain(v);
                return std::make_pair(0, handle_v[v]);
            }
            while(que.size() >= 2){
                auto [sv,vv] = que.top(); que.pop();
                auto [sw,vw] = que.top(); que.pop();
                int vx = pushNode2(TYPE_RAKE, vv, vw, v);
                que.push({ sw-1, vx });
            }
            auto [h,s] = que.top();
            handle_v[v] = pushNode1(TYPE_SHUTOUT, s, v, -4);
            return std::make_pair(-h+1, handle_v[v]);
        };
        struct HPathNode { int h; int s; int e; };
        auto dfs_h_x = [&](auto& dfs_c, auto& dfs_h, int u) -> std::pair<int,int> {
            std::vector<HPathNode> hpath;
            auto mergeBack2 = [&](){
                auto hp = hpath.back(); hpath.pop_back();
                auto hp2 = hpath.back();
                hp2.s = (handle_e[hp.e] = pushNode2(TYPE_COMPRESS, hp2.s, hp.s, hp.e));
                hp2.h++;
                hpath.back() = hp2;
            };
            for(int v=u; v>=0; v=nx[v]){
                auto [h,s] = dfs_c(dfs_c, dfs_h, v);
                int e = parentEdge[v];
                while(hpath.size() >= 2 && hpath[hpath.size()-2].h <= h) mergeBack2();
                while(!hpath.empty() && hpath.back().h <= h){
                    auto hp = hpath.back(); hpath.pop_back();
                    s = (handle_e[e] = pushNode2(TYPE_COMPRESS, hp.s, s, e));
                    h++; e = hp.e;
                }
                hpath.push_back({ h, s, e });
            }
            while(hpath.size() >= 2) mergeBack2();
            return std::make_pair(hpath.back().h, hpath.back().s);
        };
        dfs_h_x(dfs_c_x, dfs_h_x, root);
    }

    int numNodes(){ return int(nodes.size()); }
    const Node& operator[](int i) const { return nodes[i]; }
};

} // namespace nachia

#include <optional>

namespace nachia{

template<class Point, class Path>
struct StaticTopTreeSystem{
    template<
        class RakeFunc, class CompressFunc,
        class ShutoutFunc, class DangleFunc, class DegenerateFunc>
    struct StaticTopTreeSystemInst {
        RakeFunc rake;
        CompressFunc compress;
        ShutoutFunc shutout;
        DangleFunc dangle;
        DegenerateFunc degenerate;

        struct StaticTopTreeAggregation {

            union NodeData {
                int x = 0;
                Point o;
                Path l;
                NodeData(){}
                ~NodeData(){}
            };

            StaticTopTreeSystemInst sys;
            StaticTopTree sttBase;
            std::vector<NodeData> data;
            
            StaticTopTreeAggregation() {}

            void updateNode(int i){
                auto& v = sttBase[i];
                switch(v.type){
                case StaticTopTree::TYPE_RAKE: {
                    new(&data[i].o) Point(sys.rake(data[v.arg1].o, data[v.arg2].o));
                } break;
                case StaticTopTree::TYPE_DANGLE: {
                    new(&data[i].o) Point(sys.dangle(v.arg2, data[v.arg1].l));
                } break;
                case StaticTopTree::TYPE_COMPRESS: {
                    int e = v.arg3;
                    auto [w,x] = sttBase.dtree[e];
                    new(&data[i].l) Path(sys.compress(data[v.arg1].l, w, e, x, data[v.arg2].l));
                } break;
                case StaticTopTree::TYPE_SHUTOUT: {
                    new(&data[i].l) Path(sys.shutout(v.arg2, data[v.arg1].o));
                } break;
                case StaticTopTree::TYPE_GAIN: {
                    new(&data[i].l) Path(sys.degenerate(v.arg1));
                } break;
                }
            }

            StaticTopTreeAggregation(
                StaticTopTreeSystemInst xsys, const Graph& tree, int root)
                : sys(std::move(xsys))
                , sttBase(tree, root)
                , data(sttBase.numNodes())
            {
                int sn = sttBase.numNodes();
                for(int i=0; i<sn; i++) updateNode(i);
            }

            ~StaticTopTreeAggregation(){
                int sn = sttBase.numNodes();
                for(int i=0; i<sn; i++){
                    auto& v = sttBase[i];
                    switch(v.type){
                    case StaticTopTree::TYPE_RAKE:
                    case StaticTopTree::TYPE_DANGLE:
                        (&data[i].o)->~Point(); break;
                    case StaticTopTree::TYPE_COMPRESS:
                    case StaticTopTree::TYPE_SHUTOUT:
                    case StaticTopTree::TYPE_GAIN:
                        (&data[i].l)->~Path(); break;
                    }
                }
            }

            int numNodes(){ return sttBase.numNodes(); }

            Path all(){ return data[numNodes()-1].l; }

            void updateVertex(int v){
                for(int p=sttBase.handle_v[v]; p>=0; p=sttBase[p].parent) updateNode(p);
            }
            void updateEdge(int e){
                for(int p=sttBase.handle_e[e]; p>=0; p=sttBase[p].parent) updateNode(p);
            }

            Path exposed1(int v){
                int x = sttBase.handle_v[v];
                if(sttBase[x].parent < 0) return data[x].l;
                auto up = [&](auto& rec, int p, int c) -> Point {
                    std::optional<Point> mp = std::nullopt;
                    auto addRake = [&](Point mmp){
                        if(mp.has_value()){
                            mp = sys.rake(mmp, mp.value());
                        } else { mp = mmp; }
                    };
                    while(p >= 0 && sttBase[p].type == StaticTopTree::TYPE_RAKE){
                        int b = sttBase[p].arg1 ^ sttBase[p].arg2 ^ c;
                        addRake(data[b].o);
                        c = p; p = sttBase[p].parent;
                    }
                    if(p < 0) return mp.value();
                    int lpe = -1;
                    std::optional<Path> lp = std::nullopt;
                    int rpe = -1;
                    std::optional<Path> rp = std::nullopt;
                    while(p >= 0){
                        auto& v = sttBase[p];
                        if(sttBase[p].type == StaticTopTree::TYPE_COMPRESS){
                            int e = v.arg3;
                            auto [w,x] = sttBase.dtree[e];
                            if(sttBase[p].arg1 == p){
                                if(rpe >= 0){
                                    rp = sys.compress(rp.value(), w, e, x, data[v.arg2].l);
                                } else {
                                    rpe = e; rp = data[v.arg2].l;
                                }
                            } else {
                                if(lpe >= 0){
                                    lp = sys.compress(data[v.arg1].l, w, e, x, lp.value());
                                } else {
                                    lpe = e; lp = data[v.arg1].l;
                                }
                            }
                        } else {
                            int e = v.arg2;
                            auto [w,x] = sttBase.dtree[e];
                            int q = sttBase[p].parent;
                            Path qc = (sttBase[q].type == StaticTopTree::TYPE_SHUTOUT
                                        && sttBase[q].parent < 0)
                                ? sys.degenerate(sttBase[q].arg1)
                                : sys.shutout(w, rec(rec, q, p));
                            if(lpe >= 0){
                                lp = sys.compress(qc, w, e, x, lp.value());
                            } else { lpe = e; lp = qc; }
                            break;
                        }
                        c = p; p = sttBase[p].parent;
                    }
                    if(lpe >= 0) addRake(sys.dangle(lpe, lp.value().reversed()));
                    if(rpe >= 0) addRake(sys.dangle(rpe, rp.value()));
                    return mp.value();
                };
                auto pt = up(up, x, -1);
                return sys.shutout(v, pt);
            }
        };

        auto newTree(const Graph& tree, int root){
            return StaticTopTreeAggregation(*this, tree, root);
        }
    };
    
    template<
        class RakeFunc, class CompressFunc,
        class ShutoutFunc, class DangleFunc, class DegenerateFunc>
    static auto Construct(
        RakeFunc rake,
        CompressFunc compress,
        ShutoutFunc shutout,
        DangleFunc dangle,
        DegenerateFunc degenerate
    ){
        return StaticTopTreeSystemInst<RakeFunc, CompressFunc, ShutoutFunc, DangleFunc, DegenerateFunc>{
            std::move(rake), std::move(compress),
            std::move(shutout), std::move(dangle), std::move(degenerate) };
    }
};

} // namespace nachia

namespace nachia{

// ax + by = gcd(a,b)
// return ( x, - )
std::pair<long long, long long> ExtGcd(long long a, long long b){
    long long x = 1, y = 0;
    while(b){
        long long u = a / b;
        std::swap(a-=b*u, b);
        std::swap(x-=y*u, y);
    }
    return std::make_pair(x, a);
}

} // namespace nachia

namespace nachia{

template<unsigned int MOD>
struct StaticModint{
private:
    using u64 = unsigned long long;
    unsigned int x;
public:

    using my_type = StaticModint;
    template< class Elem >
    static Elem safe_mod(Elem x){
        if(x < 0){
            if(0 <= x+MOD) return x + MOD;
            return MOD - ((-(x+MOD)-1) % MOD + 1);
        }
        return x % MOD;
    }

    StaticModint() : x(0){}
    StaticModint(const my_type& a) : x(a.x){}
    StaticModint& operator=(const my_type&) = default;
    template< class Elem >
    StaticModint(Elem v) : x(safe_mod(v)){}
    unsigned int operator*() const noexcept { return x; }
    my_type& operator+=(const my_type& r) noexcept { auto t = x + r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
    my_type operator+(const my_type& r) const noexcept { my_type res = *this; return res += r; }
    my_type& operator-=(const my_type& r) noexcept { auto t = x + MOD - r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
    my_type operator-(const my_type& r) const noexcept { my_type res = *this; return res -= r; }
    my_type operator-() const noexcept { my_type res = *this; res.x = ((res.x == 0) ? 0 : (MOD - res.x)); return res; }
    my_type& operator*=(const my_type& r)noexcept { x = (u64)x * r.x % MOD; return *this; }
    my_type operator*(const my_type& r) const noexcept { my_type res = *this; return res *= r; }
    my_type pow(unsigned long long i) const noexcept {
        my_type a = *this, res = 1;
        while(i){ if(i & 1){ res *= a; } a *= a; i >>= 1; }
        return res;
    }
    my_type inv() const { return my_type(ExtGcd(x, MOD).first); }
    unsigned int val() const noexcept { return x; }
    static constexpr unsigned int mod() { return MOD; }
    static my_type raw(unsigned int val) noexcept { auto res = my_type(); res.x = val; return res; }
    my_type& operator/=(const my_type& r){ return operator*=(r.inv()); }
    my_type operator/(const my_type& r) const { return operator*(r.inv()); }
};

} // namespace nachia
#include <cstdio>
#include <cctype>
#include <cstdint>
#include <string>

namespace nachia{

struct CInStream{
private:
	static const unsigned int INPUT_BUF_SIZE = 1 << 17;
	unsigned int p = INPUT_BUF_SIZE;
	static char Q[INPUT_BUF_SIZE];
public:
	using MyType = CInStream;
	char seekChar(){
		if(p == INPUT_BUF_SIZE){
			size_t len = fread(Q, 1, INPUT_BUF_SIZE, stdin);
			if(len != INPUT_BUF_SIZE) Q[len] = '\0';
			p = 0;
		}
		return Q[p];
	}
	void skipSpace(){ while(isspace(seekChar())) p++; }
private:
	template<class T, int sp = 1>
	T nextUInt(){
		if constexpr (sp) skipSpace();
		T buf = 0;
		while(true){
			char tmp = seekChar();
			if('9' < tmp || tmp < '0') break;
			buf = buf * 10 + (tmp - '0');
			p++;
		}
		return buf;
	}
public:
	uint32_t nextU32(){ return nextUInt<uint32_t>(); }
	int32_t nextI32(){
		skipSpace();
		if(seekChar() == '-'){
			p++; return (int32_t)(-nextUInt<uint32_t, 0>());
		}
		return (int32_t)nextUInt<uint32_t, 0>();
	}
	uint64_t nextU64(){ return nextUInt<uint64_t>();}
	int64_t nextI64(){
		skipSpace();
		if(seekChar() == '-'){
			p++; return (int64_t)(-nextUInt<int64_t, 0>());
		}
		return (int64_t)nextUInt<int64_t, 0>();
	}
	template<class T>
	T nextInt(){
		skipSpace();
		if(seekChar() == '-'){
			p++;
			return - nextUInt<T, 0>();
		}
		return nextUInt<T, 0>();
	}
	char nextChar(){ skipSpace(); char buf = seekChar(); p++; return buf; }
	std::string nextToken(){
		skipSpace();
		std::string buf;
		while(true){
			char ch = seekChar();
			if(isspace(ch) || ch == '\0') break;
			buf.push_back(ch);
			p++;
		}
		return buf;
	}
	MyType& operator>>(unsigned int& dest){ dest = nextU32(); return *this; }
	MyType& operator>>(int& dest){ dest = nextI32(); return *this; }
	MyType& operator>>(unsigned long& dest){ dest = nextU64(); return *this; }
	MyType& operator>>(long& dest){ dest = nextI64(); return *this; }
	MyType& operator>>(unsigned long long& dest){ dest = nextU64(); return *this; }
	MyType& operator>>(long long& dest){ dest = nextI64(); return *this; }
	MyType& operator>>(std::string& dest){ dest = nextToken(); return *this; }
	MyType& operator>>(char& dest){ dest = nextChar(); return *this; }
} cin;

struct FastOutputTable{
	char LZ[1000][4] = {};
	char NLZ[1000][4] = {};
	constexpr FastOutputTable(){
		using u32 = uint_fast32_t;
		for(u32 d=0; d<1000; d++){
			LZ[d][0] = ('0' + d / 100 % 10);
			LZ[d][1] = ('0' + d /  10 % 10);
			LZ[d][2] = ('0' + d /   1 % 10);
			LZ[d][3] = '\0';
		}
		for(u32 d=0; d<1000; d++){
			u32 i = 0;
			if(d >= 100) NLZ[d][i++] = ('0' + d / 100 % 10);
			if(d >=  10) NLZ[d][i++] = ('0' + d /  10 % 10);
			if(d >=   1) NLZ[d][i++] = ('0' + d /   1 % 10);
			NLZ[d][i++] = '\0';
		}
	}
};

struct COutStream{
private:
	using u32 = uint32_t;
	using u64 = uint64_t;
	using MyType = COutStream;
	static const u32 OUTPUT_BUF_SIZE = 1 << 17;
	static char Q[OUTPUT_BUF_SIZE];
	static constexpr FastOutputTable TB = FastOutputTable();
	u32 p = 0;
	static constexpr u32 P10(u32 d){ return d ? P10(d-1)*10 : 1; }
	static constexpr u64 P10L(u32 d){ return d ? P10L(d-1)*10 : 1; }
	template<class T, class U> static void Fil(T& m, U& l, U x){ m = l/x; l -= m*x; }
public:
	void next_dig9(u32 x){
		u32 y;
		Fil(y, x, P10(6));
		nextCstr(TB.LZ[y]);
		Fil(y, x, P10(3));
		nextCstr(TB.LZ[y]); nextCstr(TB.LZ[x]);
	}
	void nextChar(char c){
		Q[p++] = c;
		if(p == OUTPUT_BUF_SIZE){ fwrite(Q, p, 1, stdout); p = 0; }
	}
	void nextEoln(){ nextChar('\n'); }
	void nextCstr(const char* s){ while(*s) nextChar(*(s++)); }
	void nextU32(uint32_t x){
		u32 y = 0;
		if(x >= P10(9)){
			Fil(y, x, P10(9));
			nextCstr(TB.NLZ[y]); next_dig9(x);
		}
		else if(x >= P10(6)){
			Fil(y, x, P10(6));
			nextCstr(TB.NLZ[y]);
			Fil(y, x, P10(3));
			nextCstr(TB.LZ[y]); nextCstr(TB.LZ[x]);
		}
		else if(x >= P10(3)){
			Fil(y, x, P10(3));
			nextCstr(TB.NLZ[y]); nextCstr(TB.LZ[x]);
		}
		else if(x >= 1) nextCstr(TB.NLZ[x]);
		else nextChar('0');
	}
	void nextI32(int32_t x){
		if(x >= 0) nextU32(x);
		else{ nextChar('-'); nextU32((u32)-x); }
	}
	void nextU64(uint64_t x){
		u32 y = 0;
		if(x >= P10L(18)){
			Fil(y, x, P10L(18));
			nextU32(y);
			Fil(y, x, P10L(9));
			next_dig9(y); next_dig9(x);
		}
		else if(x >= P10L(9)){
			Fil(y, x, P10L(9));
			nextU32(y); next_dig9(x);
		}
		else nextU32(x);
	}
	void nextI64(int64_t x){
		if(x >= 0) nextU64(x);
		else{ nextChar('-'); nextU64((u64)-x); }
	}
	template<class T>
	void nextInt(T x){
		if(x < 0){ nextChar('-'); x = -x; }
		if(!(0 < x)){ nextChar('0'); return; }
		std::string buf;
		while(0 < x){
			buf.push_back('0' + (int)(x % 10));
			x /= 10;
		}
		for(int i=(int)buf.size()-1; i>=0; i--){
			nextChar(buf[i]);
		}
	}
	void writeToFile(bool flush = false){
		fwrite(Q, p, 1, stdout);
		if(flush) fflush(stdout);
		p = 0;
	}
	COutStream(){ Q[0] = 0; }
	~COutStream(){ writeToFile(); }
	MyType& operator<<(unsigned int tg){ nextU32(tg); return *this; }
	MyType& operator<<(unsigned long tg){ nextU64(tg); return *this; }
	MyType& operator<<(unsigned long long tg){ nextU64(tg); return *this; }
	MyType& operator<<(int tg){ nextI32(tg); return *this; }
	MyType& operator<<(long tg){ nextI64(tg); return *this; }
	MyType& operator<<(long long tg){ nextI64(tg); return *this; }
	MyType& operator<<(const std::string& tg){ nextCstr(tg.c_str()); return *this; }
	MyType& operator<<(const char* tg){ nextCstr(tg); return *this; }
	MyType& operator<<(char tg){ nextChar(tg); return *this; }
} cout;

char CInStream::Q[INPUT_BUF_SIZE];
char COutStream::Q[OUTPUT_BUF_SIZE];

} // namespace nachia

int main(){
    using nachia::cin;
    using nachia::cout;
    int N; cin >> N;
    auto tree = nachia::Graph(N, true);

    using u64 = uint64_t;

    struct Point {
        std::array<u64, 2> cnt;
        std::array<u64, 2> sum;
        u64 ans;
    };
    struct Path {
        std::array<u64, 2> cnt;
        std::array<u64, 2> ls;
        std::array<u64, 2> rs;
        u64 ans;
        u64 len;
    };
    for(int i=0; i<N-1; i++){
        int u,v; cin >> u >> v;
        u--;
        v--;
        tree.addEdge(u,v);
    }
    std::vector<std::vector<int>> h(N);
    for (int i = 1; i < N; ++i) {
        int u, v;
        cin >> u >> v;
        u--;
        v--;
        h[u].push_back(v);
        h[v].push_back(u);
    }
    auto hld = [&](auto self, int v) -> int {
        int s = 1;
        int key = 0;
        for (std::size_t j = 0; j < h[v].size(); ++j) {
            const int u = h[v][j];
            for (std::size_t i = 0; i < h[u].size(); ++i) {
                if (h[u][i] == v) {
                    h[u].erase(h[u].begin() + i);
                    break;
                }
            }
            int k = self(self, u);
            if (k > key) {
                if (j > 0) {
                    std::swap(h[v][0], h[v][j]);
                }
                key = k;
            }
            s += k;
        }
        return s;
    };
    hld(hld, 0);

    std::vector<int> vertex(N, 0);
    auto sys = nachia::StaticTopTreeSystem<Point, Path>::Construct(
        [](Point a, Point b) -> Point {
            Point c;
            c.ans = a.ans + b.ans;
            for (int i = 0; i < 2; ++i) {
                c.cnt[i] = a.cnt[i] + b.cnt[i];
                c.sum[i] = a.sum[i] + b.sum[i];
                c.ans += a.cnt[i] * b.sum[i ^ 1];
                c.ans += a.sum[i] * b.cnt[i ^ 1];
            }
            return c;
        },
        [&](Path a, int u, int e, int v, Path b) -> Path {
            Path c;
            c.ans = a.ans + b.ans;
            c.len = a.len + b.len + 1;
            for (int i = 0; i < 2; ++i) {
                c.cnt[i] = a.cnt[i] + b.cnt[i];
                c.ls[i] = a.ls[i] + b.ls[i] + (1 + a.len) * b.cnt[i];
                c.rs[i] = a.rs[i] + (1 + b.len) * a.cnt[i] + b.rs[i];
                c.ans += a.cnt[i] * b.cnt[i ^ 1];
                c.ans += a.cnt[i] * b.ls[i ^ 1];
                c.ans += a.rs[i] * b.cnt[i ^ 1];
            }
            return c;
        },
        [&](int v, Point p) -> Path {
            Path c;
            c.cnt = p.cnt;
            c.ls = p.sum;
            c.rs = p.sum;
            c.ans = p.ans;
            c.len = 0;
            const auto x = vertex[v];
            c.ans += p.sum[x ^ 1];
            c.cnt[x] += 1;
            return c;
        },
        [&](int e, Path p) -> Point {
            Point c;
            c.cnt = p.cnt;
            c.sum = {p.ls[0] + p.cnt[0], p.ls[1] + p.cnt[1]};
            c.ans = p.ans;
            return c;
        },
        [&](int v) -> Path {
            Path c;
            c.cnt = {0, 0};
            c.ls = {0, 0};
            c.rs = {0, 0};
            c.ans = c.len = 0;
            const auto x = vertex[v];
            c.cnt[x] += 1;
            return c;
        }
    );
    auto stt = sys.newTree(tree, 0);
    stt.all();
    auto flip = [&](auto self, int v) -> void {
        vertex[v] ^= 1;
        stt.updateVertex(v);
        for (const auto u : h[v]) {
            self(self, u);
        }
    };
    u64 ans = 0;
    auto sack = [&](auto self, int v, bool save) -> void {
        for (std::size_t j = h[v].size(); j > 0; --j) {
            self(self, h[v][j - 1], j == 1);
        }
        for (std::size_t j = 1; j < h[v].size(); ++j) {
            flip(flip, h[v][j]);
        }
        vertex[v] ^= 1;
        stt.updateVertex(v);
        auto val = stt.all();
        ans += val.ans;
        if (!save) {
            flip(flip, v);
        }
    };
    sack(sack, 0, true);
    cout << ans * 2 << "\n";
    return 0;
}