#include <bits/stdc++.h>
using namespace std;
template<typename T_container, typename T = typename enable_if<!is_same<T_container, string>::value, typename T_container::value_type>::type> ostream& operator<<(ostream &os, const T_container &v) { os << '{'; string sep; for (const T &x : v) os << sep << x, sep = ", "; return os << '}'; }
void dbg_out() { cerr << endl; }
template<typename Head, typename... Tail> void dbg_out(Head H, Tail... T) { cerr << ' ' << H; dbg_out(T...); }
#ifdef ONPC
#define deb(...) cerr << '[' << __FILE__ << ':' << __LINE__ << "] (" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#define deb(...)
#endif
// c++ short types
#define vt vector
//typedef long long ll;
typedef long double ld;
void whattime() { cout << "finished in " << clock() * 1.0 / CLOCKS_PER_SEC << " sec" << endl; }
// const int mod = 1e9 + 7;
const int mod = 998244353;
const int inf = 1e9;
const int64_t infll = 1e13;
bool debug = false;
const ld eps = 1e-9;
const ld pi = acos(-1);
mt19937_64 rng((int) chrono::steady_clock::now().time_since_epoch().count());
uint64_t h(uint64_t x) {
return x * x * x * 1237123 + 19260817;
}
uint64_t f(uint64_t x) {
int64_t cur = h(x & ((1 << 31) - 1)) + h(x >> 31);
return cur;
}
vector<vector<int>> adj;
vector<bool> visited;
vector<int> parent;
int cycle_start, cycle_end;
bool dfs(int v, int par) { // passing vertex and its parent vertex
visited[v] = true;
for (int u : adj[v]) {
if(u == par) continue; // skipping edge to parent vertex
if (visited[u]) {
cycle_end = v;
cycle_start = u;
return true;
}
parent[u] = v;
if (dfs(u, parent[u]))
return true;
}
return false;
}
vt<int> find_cycle(int n) {
visited.assign(n, false);
parent.assign(n, -1);
cycle_start = -1;
for (int v = 0; v < n; v++) {
if (!visited[v] && dfs(v, parent[v]))
break;
}
if (cycle_start == -1) {
assert(false);
} else {
vector<int> cycle;
cycle.push_back(cycle_start);
for (int v = cycle_end; v != cycle_start; v = parent[v])
cycle.push_back(v);
cycle.push_back(cycle_start);
return cycle;
}
return {};
}
vt<uint64_t> get(vt<vt<int>> g) {
int n = (int)g.size();
adj = g;
vt<int> cycle = find_cycle(n);
vt<int> is_cycle(n, false);
for(auto x: cycle) {
is_cycle[x] = true;
}
vt<uint64_t> res;
cycle.pop_back();
int id = 0;
map<vt<int>, int> ha;
for(auto i: cycle) {
auto Dfs = [&](auto self, int e, int p) -> int {
vt<int> hs;
for(auto to:g[e]) if(to != p and !is_cycle[to]) {
hs.push_back(self(self,to,e));
}
sort(hs.begin(), hs.end());
if(ha.count(hs)) {
return ha[hs];
}
return ha[hs] = id++;
};
res.push_back(Dfs(Dfs, i, i));
}
return res;
}
void solve() {
int n; cin >> n;
vt<vt<int>> g(n);
for(int i = 0; i < n; ++i) {
int a, b; cin >> a >> b;
g[--a].push_back(--b);
g[b].push_back(a);
}
vt<uint64_t> a = get(g);
for(auto &v: g) {
v.clear();
}
for(int i = 0; i < n; ++i) {
int a, b; cin >> a >> b;
g[--a].push_back(--b);
g[b].push_back(a);
}
vt<uint64_t> b = get(g);
if(a.size() != b.size()) {
cout << "No\n";
return ;
}
{
vt<uint64_t> c = a, d = b;
sort(c.begin(), c.end());
sort(d.begin(), d.end());
if(c != d) {
cout << "No\n";
return;
}
map<uint64_t, int> ids;
for(auto x: c) {
ids[x];
}
int id = 0;
for(auto& [val, i]: ids) {
i = id++;
}
for(auto &x: a) {
x = ids[x];
}
for(auto &x: b) {
x = ids[x];
}
}
const int m = 1e9 + 123;
const int m1 = 1e9 +123, m2 = 1e9 + 7;
const int p1 = rand() % (m1 - 256) + 256;
const int p2 = rand() % (m2 - 256) + 256;
int k = (int)a.size();
vt<vt<int>> pw(k, vt<int>(2, 1));
for(int i = 1; i < k; ++i) {
pw[i][0] = (pw[i-1][0] * 1ll * p1) % m1;
pw[i][1] = (pw[i-1][1] * 1ll * p1) % m1;
}
{
array<int, 2> hash = {0,0};
for(auto x: a) {
hash[0] = (hash[0] * 1ll * p1 + x) % m1;
hash[1] = (hash[1] * 1ll * p2 + x) % m2;
}
vt<array<int, 2>> pref(k, {0,0});
for(int i = 0; i < k; ++i) {
pref[i][0] = pw[i][0] * 1ll * b[i] % m1;
pref[i][1] = pw[i][1] * 1ll * b[i] % m2;
if(i) {
pref[i][0] = (pref[i][0] + pref[i-1][0]) % m1;
pref[i][1] = (pref[i][1] + pref[i-1][1]) % m2;
}
}
if(pref.back() == hash) {
cout << "Yes\n";
return ;
}
array<int, 2> cur = {0, 0};
for(int i = k - 1; i >= 1; --i) {
cur[0] = (cur[0] * 1ll * p + b[i]) % m1;
cur[1] = (cur[1] * 1ll * p + b[i]) % m2;
auto z = cur;
z[0] = (z[0] + pw[k-i][0] * 1ll * pref[i-1][0]) % m1;
z[1] = (z[1] + pw[k-i][1] * 1ll * pref[i-1][1]) % m2;
if(z == hash) {
cout << "Yes\n";
return ;
}
}
}
{
array<int, 2> hash = {0,0};
for(auto x: a) {
hash[0] = (hash[0] * 1ll * p1 + x) % m1;
hash[1] = (hash[1] * 1ll * p2 + x) % m2;
}
vt<array<int, 2>> pref(k, {0,0});
for(int i = 0; i < k; ++i) {
pref[i][0] = pw[i][0] * 1ll * b[i] % m1;
pref[i][1] = pw[i][1] * 1ll * b[i] % m2;
if(i) {
pref[i][0] = (pref[i][0] + pref[i-1][0]) % m1;
pref[i][1] = (pref[i][1] + pref[i-1][1]) % m2;
}
}
if(pref.back() == hash) {
cout << "Yes\n";
return ;
}
array<int, 2> cur = {0, 0};
for(int i = k - 1; i >= 1; --i) {
cur[0] = (cur[0] * 1ll * p + b[i]) % m1;
cur[1] = (cur[1] * 1ll * p + b[i]) % m2;
auto z = cur;
z[0] = (z[0] + pw[k-i][0] * 1ll * pref[i-1][0]) % m1;
z[1] = (z[1] + pw[k-i][1] * 1ll * pref[i-1][1]) % m2;
if(z == hash) {
cout << "Yes\n";
return ;
}
}
}
deb(a, b);
reverse(a.begin(), a.end());
cout << "No\n";
}
int main()
{
ios::sync_with_stdio(false); cin.tie(nullptr);
int tt = 1;;
if(debug) {
tt = 1e3;
} else {
}
for(int t = 0; t < tt; ++t) {
solve();
}
#ifdef ONPC
whattime();
#endif
return 0;
}