#include <iostream> #include <vector> #include <unordered_map> #include <tuple> using namespace std; struct Edge { int u, v; Edge(int a, int b) : u(min(a, b)), v(max(a, b)) {} bool operator==(const Edge& other) const { return u == other.u && v == other.v; } }; namespace std { template<> struct hash<Edge> { size_t operator()(const Edge& e) const { return hash<long long>()( (static_cast<long long>(e.u) << 32) ^ e.v ); } }; } struct UnionFind { vector<int> parent; vector<int> rank; vector<int> weight; // 权重表示相对方向 UnionFind(int n) : parent(n), rank(n, 0), weight(n, 0) { for (int i = 0; i < n; ++i) parent[i] = i; } int find(int x) { if (parent[x] != x) { int root = find(parent[x]); weight[x] ^= weight[parent[x]]; parent[x] = root; } return parent[x]; } bool unite(int x, int y, int w) { int px = find(x); int py = find(y); if (px == py) { return (weight[x] ^ weight[y]) == w; } if (rank[px] < rank[py]) { swap(px, py); swap(x, y); w ^= 1; // 方向交换需要翻转权重 } parent[py] = px; weight[py] = weight[y] ^ w ^ weight[x]; if (rank[px] == rank[py]) rank[px]++; return true; } }; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int M; cin >> M; unordered_map<Edge, vector<int>> edgeMap; vector<tuple<int, int, int>> triangles(M); for (int i = 0; i < M; ++i) { int a, b, c; cin >> a >> b >> c; triangles[i] = {a, b, c}; edgeMap[Edge(a, b)].push_back(i); edgeMap[Edge(b, c)].push_back(i); edgeMap[Edge(a, c)].push_back(i); } for (const auto& [e, tris] : edgeMap) { if (tris.size() > 2) { cout << "NO\n"; return 0; } } UnionFind uf(M); bool possible = true; for (const auto& [e, tris] : edgeMap) { if (tris.size() == 2) { int u = tris[0], v = tris[1]; if (!uf.unite(u, v, 1)) { // 共享边需要方向相反 possible = false; break; } } } cout << (possible ? "YES" : "NO") << endl; return 0; }