#include <iostream> #include <iomanip> #include <cassert> #include <vector> #include <algorithm> #include <utility> #include <set> #include <cstdint> #include <cstddef> namespace zawa { using i16 = std::int16_t; using i32 = std::int32_t; using i64 = std::int64_t; using i128 = __int128_t; using u8 = std::uint8_t; using u16 = std::uint16_t; using u32 = std::uint32_t; using u64 = std::uint64_t; using usize = std::size_t; } // namespace zawa #include <iterator> #include <limits> namespace zawa { template <class T> class CompressedSequence { private: std::vector<T> comped_; std::vector<u32> f_; public: static constexpr u32 NotFound = std::numeric_limits<u32>::max(); CompressedSequence() = default; template <class InputIterator> CompressedSequence(InputIterator first, InputIterator last) : comped_(first, last), f_{} { std::sort(comped_.begin(), comped_.end()); comped_.erase(std::unique(comped_.begin(), comped_.end()), comped_.end()); comped_.shrink_to_fit(); f_.reserve(std::distance(first, last)); for (auto it{first} ; it != last ; it++) { f_.emplace_back(std::distance(comped_.begin(), std::lower_bound(comped_.begin(), comped_.end(), *it))); } } CompressedSequence(const std::vector<T>& A) : CompressedSequence(A.begin(), A.end()) {} inline usize size() const noexcept { return comped_.size(); } u32 operator[](const T& v) const { return std::distance(comped_.begin(), std::lower_bound(comped_.begin(), comped_.end(), v)); } u32 find(const T& v) const { u32 i = std::distance(comped_.begin(), std::lower_bound(comped_.begin(), comped_.end(), v)); return i == comped_.size() or comped_[i] != v ? NotFound : i; } bool contains(const T& v) const { u32 i = std::distance(comped_.begin(), std::lower_bound(comped_.begin(), comped_.end(), v)); return i < comped_.size() and comped_[i] == v; } u32 at(const T& v) const { u32 res{(*this)[v]}; assert(res < size() and comped_[res] == v); return res; } inline u32 map(u32 i) const noexcept { assert(i < f_.size()); return f_[i]; } inline T inverse(u32 i) const noexcept { assert(i < size()); return comped_[i]; } }; } // namespace zawa std::ostream& operator<<(std::ostream& os, std::pair<int, int> p) { os << '[' << p.first << ',' << p.second << ']'; return os; } using namespace zawa; int N, A[100010], B[100010], C[100010]; std::vector<std::pair<int, std::pair<int, int>>> g[100010]; bool solve() { std::vector<std::pair<int, int>> app; for (int i = 0 ; i < N ; i++) { app.push_back({A[i], B[i]}); app.push_back({B[i], C[i]}); app.push_back({A[i], C[i]}); } CompressedSequence comp{app}; std::vector<std::vector<int>> vals(comp.size()); for (int i = 0 ; i < N ; i++) { for (const auto& p : {std::pair{A[i], B[i]}, std::pair{B[i], C[i]}, std::pair{A[i], C[i]}}) { assert(p.first < p.second); auto it = comp.at(p); vals[it].push_back(i); } } for (int i = 0 ; i < (int)comp.size() ; i++) { if (vals[i].size() >= 3u) return false; if (vals[i].size() == 1u) continue; g[vals[i][0]].push_back({vals[i][1], comp.inverse(i)}); g[vals[i][1]].push_back({vals[i][0], comp.inverse(i)}); } std::vector<int> col(comp.size(), -1); auto assign = [&](int i, int c) -> bool { assert(0 <= i and i < (int)comp.size()); // std::cout << "try " << comp.inverse(i) << ' ' << c << std::endl; if (col[i] == -1) col[i] = c; else { if (col[i] == c) return false; } return true; }; // 0 hueru // 1 heru std::vector<bool> vis(N); auto dfs = [&](auto dfs, int v, int c) -> bool { // std::cout << "dfs " << A[v] << ' ' << B[v] << ' ' << C[v] << " col " << c << std::endl; if (!assign(comp.find({A[v], B[v]}), c)) return false; if (!assign(comp.find({B[v], C[v]}), c)) return false; if (!assign(comp.find({A[v], C[v]}), c ^ 1)) return false; vis[v] = true; for (const auto& [x, e] : g[v]) if (!vis[x]) { auto it = comp.at(e); int nc = col[it] ^ 1; if (e == std::pair{A[x], C[x]}) nc ^= 1; if (!dfs(dfs, x, nc)) return false; } return true; }; for (int i = 0 ; i < N ; i++) if (!vis[i]) { if (!dfs(dfs, i, 0)) return false; } return true; } int main() { std::cin.tie(nullptr)->sync_with_stdio(false); std::cin >> N; for (int i = 0 ; i < N ; i++) std::cin >> A[i] >> B[i] >> C[i]; std::cout << (solve() ? "YES\n" : "NO\n"); }