Problem p03726 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned int;
using pcc = pair<char, char>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<double, double>;
using tuplis = array<ll, 3>;
template <class T> using pq = priority_queue<T, vector<T>, greater<T>>;
const ll LINF = 0x1fffffffffffffff;
const ll MINF = 0x7fffffffffff;
const int INF = 0x3fffffff;
const int MOD = 1000000007;
const int MODD = 998244353;
const ld DINF = numeric_limits<ld>::infinity();
const ld EPS = 1e-9;
const ld PI = 3.1415926535897932;
const ll four[] = {0, 1, 0, -1, 0};
const ll eight[] = {0, 1, 1, 0, -1, -1, 1, -1, 0};
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload3(_1, _2, _3, name, ...) name
#define rep1(n) for (ll i = 0; i < n; ++i)
#define rep2(i, n) for (ll i = 0; i < n; ++i)
#define rep3(i, a, b) for (ll i = a; i < b; ++i)
#define rep4(i, a, b, c) for (ll i = a; i < b; i += c)
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(n) for (ll i = (n)-1; i >= 0; i--)
#define rrep2(i, n) for (ll i = (n)-1; i >= 0; i--)
#define rrep3(i, a, b) for (ll i = (b)-1; i >= (a); i--)
#define rrep4(i, a, b, c) for (ll i = a + (b - a - 1) / c * c; i >= a; i -= c)
#define rrep(...)                                                              \
  overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define each(i, a) for (auto &&i : a)
#define all1(i) begin(i), end(i)
#define all2(i, a) begin(i), begin(i) + a
#define all3(i, a, b) begin(i) + a, begin(i) + b
#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)
#define rall1(i) (i).rbegin(), (i).rend()
#define rall2(i, k) (i).rbegin(), (i).rbegin() + k
#define rall3(i, a, b) (i).rbegin() + a, (i).rbegin() + b
#define rall(...) overload3(__VA_ARGS__, rall3, rall2, rall1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__), 0LL)
#define dsum(...) accumulate(all(__VA_ARGS__), 0.0L)
#define elif else if
#define unless(a) if (!(a))
#define mp make_pair
#define mt make_tuple
#define INT(...)                                                               \
  int __VA_ARGS__;                                                             \
  in(__VA_ARGS__)
#define LL(...)                                                                \
  ll __VA_ARGS__;                                                              \
  in(__VA_ARGS__)
#define ULL(...)                                                               \
  ull __VA_ARGS__;                                                             \
  in(__VA_ARGS__)
#define STR(...)                                                               \
  string __VA_ARGS__;                                                          \
  in(__VA_ARGS__)
#define CHR(...)                                                               \
  char __VA_ARGS__;                                                            \
  in(__VA_ARGS__)
#define DBL(...)                                                               \
  double __VA_ARGS__;                                                          \
  in(__VA_ARGS__)
#define LD(...)                                                                \
  ld __VA_ARGS__;                                                              \
  in(__VA_ARGS__)
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define VEC(type, name, size)                                                  \
  vector<type> name(size);                                                     \
  in(name)
#define vv(type, name, h, ...)                                                 \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define VV(type, name, h, w)                                                   \
  vector<vector<type>> name(h, vector<type>(w));                               \
  in(name)
#define vvv(type, name, h, w, ...)                                             \
  vector<vector<vector<type>>> name(                                           \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
template <class T> auto max(const T &a) { return *max_element(all(a)); }
template <class T> auto min(const T &a) { return *min_element(all(a)); }
ll gcd(ll a, ll b) {
  while (b) {
    ll c = b;
    b = a % b;
    a = c;
  }
  return a;
}
ll lcm(ll a, ll b) {
  if (!a || !b)
    return 0;
  return a * b / gcd(a, b);
}
ll intpow(ll a, ll b) {
  ll ans = 1;
  while (b) {
    if (b & 1)
      ans *= a;
    a *= a;
    b /= 2;
  }
  return ans;
}
ll modpow(ll a, ll b, ll p) {
  ll ans = 1;
  while (b) {
    if (b & 1)
      (ans *= a) %= p;
    (a *= a) %= p;
    b /= 2;
  }
  return ans;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
vector<pll> factor(ull x) {
  vector<pll> ans;
  for (ll i = 2; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back({i, 1});
      while ((x /= i) % i == 0)
        ans.back().second++;
    }
  if (x != 1)
    ans.push_back({x, 1});
  return ans;
}
vector<ll> divisor(ull x) {
  vector<ll> ans;
  for (ll i = 1; i * i <= x; i++)
    if (x % i == 0)
      ans.push_back(i);
  rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]);
  return ans;
}
template <class T> unordered_map<T, ll> press(vector<T> &a) {
  auto b = a;
  sort(all(b));
  b.erase(unique(all(b)), b.end());
  unordered_map<T, ll> ans;
  rep(b.size()) ans[b[i]] = i;
  each(i, a) i = ans[i];
  return ans;
}
template <class T> map<T, ll> press_map(vector<T> &a) {
  auto b = a;
  sort(all(b));
  b.erase(unique(all(b)), b.end());
  map<T, ll> ans;
  rep(b.size()) ans[b[i]] = i;
  each(i, a) i = ans[i];
  return ans;
}
int scan() { return getchar(); }
void scan(int &a) { scanf("%d", &a); }
void scan(unsigned &a) { scanf("%u", &a); }
void scan(long &a) { scanf("%ld", &a); }
void scan(long long &a) { scanf("%lld", &a); }
void scan(unsigned long long &a) { scanf("%llu", &a); }
void scan(char &a) {
  do {
    a = getchar();
  } while (a == ' ' || a == '\n');
}
void scan(float &a) { scanf("%f", &a); }
void scan(double &a) { scanf("%lf", &a); }
void scan(long double &a) { scanf("%Lf", &a); }
void scan(vector<bool> &a) {
  for (unsigned i = 0; i < a.size(); i++) {
    int b;
    scan(b);
    a[i] = b;
  }
}
void scan(char a[]) { scanf("%s", a); }
void scan(string &a) { cin >> a; }
template <class T> void scan(vector<T> &);
template <class T, size_t size> void scan(array<T, size> &);
template <class T, class L> void scan(pair<T, L> &);
template <class T, size_t size> void scan(T (&)[size]);
template <class T> void scan(vector<T> &a) {
  for (auto &&i : a)
    scan(i);
}
template <class T> void scan(deque<T> &a) {
  for (auto &&i : a)
    scan(i);
}
template <class T, size_t size> void scan(array<T, size> &a) {
  for (auto &&i : a)
    scan(i);
}
template <class T, class L> void scan(pair<T, L> &p) {
  scan(p.first);
  scan(p.second);
}
template <class T, size_t size> void scan(T (&a)[size]) {
  for (auto &&i : a)
    scan(i);
}
template <class T> void scan(T &a) { cin >> a; }
void in() {}
template <class Head, class... Tail> void in(Head &head, Tail &...tail) {
  scan(head);
  in(tail...);
}
void print() { putchar(' '); }
void print(bool a) { printf("%d", a); }
void print(int a) { printf("%d", a); }
void print(unsigned a) { printf("%u", a); }
void print(long a) { printf("%ld", a); }
void print(long long a) { printf("%lld", a); }
void print(unsigned long long a) { printf("%llu", a); }
void print(char a) { printf("%c", a); }
void print(char a[]) { printf("%s", a); }
void print(const char a[]) { printf("%s", a); }
void print(float a) { printf("%.15f", a); }
void print(double a) { printf("%.15f", a); }
void print(long double a) { printf("%.15Lf", a); }
void print(const string &a) {
  for (auto &&i : a)
    print(i);
}
template <class T> void print(const vector<T> &);
template <class T, size_t size> void print(const array<T, size> &);
template <class T, class L> void print(const pair<T, L> &p);
template <class T, size_t size> void print(const T (&)[size]);
template <class T> void print(const vector<T> &a) {
  if (a.empty())
    return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    putchar(' ');
    print(*i);
  }
}
template <class T> void print(const deque<T> &a) {
  if (a.empty())
    return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    putchar(' ');
    print(*i);
  }
}
template <class T, size_t size> void print(const array<T, size> &a) {
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    putchar(' ');
    print(*i);
  }
}
template <class T, class L> void print(const pair<T, L> &p) {
  print(p.first);
  putchar(' ');
  print(p.second);
}
template <class T, size_t size> void print(const T (&a)[size]) {
  print(a[0]);
  for (auto i = a; ++i != end(a);) {
    putchar(' ');
    print(*i);
  }
}
template <class T> void print(const T &a) { cout << a; }
int out() {
  putchar('\n');
  return 0;
}
template <class T> int out(const T &t) {
  print(t);
  putchar('\n');
  return 0;
}
template <class Head, class... Tail>
int out(const Head &head, const Tail &...tail) {
  print(head);
  putchar(' ');
  out(tail...);
  return 0;
}
#ifdef DEBUG
void err() { putchar('\n'); }
template <class T> void err(const T &t) {
  print(t);
  putchar('\n');
}
template <class Head, class... Tail>
void err(const Head &head, const Tail &...tail) {
  print(head);
  putchar(' ');
  out(tail...);
}
#else
template <class... T> void err(const T &...) {}
#endif
int first(bool i = true) { return out(i ? "first" : "second"); }
int yes(bool i = true) { return out(i ? "yes" : "no"); }
int Yes(bool i = true) { return out(i ? "Yes" : "No"); }
int No() { return out("No"); }
int YES(bool i = true) { return out(i ? "YES" : "NO"); }
int NO() { return out("NO"); }
int Yay(bool i = true) { return out(i ? "Yay!" : ":("); }
int possible(bool i = true) { return out(i ? "possible" : "impossible"); }
int Possible(bool i = true) { return out(i ? "Possible" : "Impossible"); }
int POSSIBLE(bool i = true) { return out(i ? "POSSIBLE" : "IMPOSSIBLE"); }
void Case(ll i) { printf("Case #%lld: ", i); }

signed main() {
  LL(n);
  if (n == 1)
    return out("First");
  vec(vector<ll>, g, n);
  vec(ll, d, n);
  rep(n - 1) {
    LL(a, b);
    a--;
    b--;
    g[a].push_back(b);
    g[b].push_back(a);
    d[a]++;
    d[b]++;
  }
  ll root = 0;
  rep(n) if (d[i] == 1) root = i;
  vec(unordered_set<ll>, child, n);
  vec(ll, parent, n);
  auto dfs = [&](ll from, ll at, auto f) -> void {
    each(i, g[at]) if (i != from) {
      child[at].insert(i);
      parent[i] = at;
      f(at, i, f);
    }
  };
  dfs(-1, root, dfs);
  queue<ll> q;
  rep(n) q.push(i);
  vec(bool, deleted, n);
  while (q.size()) {
    ll at = q.front();
    q.pop();
    ll p, c;
    if (d[at] == 1 && at != root) {
      p = parent[at];
      c = at;
      if (d[p] < 1 || 2 < d[p])
        continue;
    }
    elif (d[at] == 2 || at == root) {
      p = at;
      c = *child[at].begin();
      if (d[c] != 1)
        continue;
    }
    else continue;
    if (deleted[p] || deleted[c])
      continue;
    each(i, g[p]) d[i]--;
    each(i, g[c]) d[i]--;
    child[parent[p]].erase(p);
    deleted[p] = deleted[c] = 1;
    q.push(parent[p]);
  }
  each(i, d) if (i) return out("First");
  out("Second");
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned int;
using pcc = pair<char, char>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<double, double>;
using tuplis = array<ll, 3>;
template <class T> using pq = priority_queue<T, vector<T>, greater<T>>;
const ll LINF = 0x1fffffffffffffff;
const ll MINF = 0x7fffffffffff;
const int INF = 0x3fffffff;
const int MOD = 1000000007;
const int MODD = 998244353;
const ld DINF = numeric_limits<ld>::infinity();
const ld EPS = 1e-9;
const ld PI = 3.1415926535897932;
const ll four[] = {0, 1, 0, -1, 0};
const ll eight[] = {0, 1, 1, 0, -1, -1, 1, -1, 0};
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload3(_1, _2, _3, name, ...) name
#define rep1(n) for (ll i = 0; i < n; ++i)
#define rep2(i, n) for (ll i = 0; i < n; ++i)
#define rep3(i, a, b) for (ll i = a; i < b; ++i)
#define rep4(i, a, b, c) for (ll i = a; i < b; i += c)
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(n) for (ll i = (n)-1; i >= 0; i--)
#define rrep2(i, n) for (ll i = (n)-1; i >= 0; i--)
#define rrep3(i, a, b) for (ll i = (b)-1; i >= (a); i--)
#define rrep4(i, a, b, c) for (ll i = a + (b - a - 1) / c * c; i >= a; i -= c)
#define rrep(...)                                                              \
  overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define each(i, a) for (auto &&i : a)
#define all1(i) begin(i), end(i)
#define all2(i, a) begin(i), begin(i) + a
#define all3(i, a, b) begin(i) + a, begin(i) + b
#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)
#define rall1(i) (i).rbegin(), (i).rend()
#define rall2(i, k) (i).rbegin(), (i).rbegin() + k
#define rall3(i, a, b) (i).rbegin() + a, (i).rbegin() + b
#define rall(...) overload3(__VA_ARGS__, rall3, rall2, rall1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__), 0LL)
#define dsum(...) accumulate(all(__VA_ARGS__), 0.0L)
#define elif else if
#define unless(a) if (!(a))
#define mp make_pair
#define mt make_tuple
#define INT(...)                                                               \
  int __VA_ARGS__;                                                             \
  in(__VA_ARGS__)
#define LL(...)                                                                \
  ll __VA_ARGS__;                                                              \
  in(__VA_ARGS__)
#define ULL(...)                                                               \
  ull __VA_ARGS__;                                                             \
  in(__VA_ARGS__)
#define STR(...)                                                               \
  string __VA_ARGS__;                                                          \
  in(__VA_ARGS__)
#define CHR(...)                                                               \
  char __VA_ARGS__;                                                            \
  in(__VA_ARGS__)
#define DBL(...)                                                               \
  double __VA_ARGS__;                                                          \
  in(__VA_ARGS__)
#define LD(...)                                                                \
  ld __VA_ARGS__;                                                              \
  in(__VA_ARGS__)
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define VEC(type, name, size)                                                  \
  vector<type> name(size);                                                     \
  in(name)
#define vv(type, name, h, ...)                                                 \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define VV(type, name, h, w)                                                   \
  vector<vector<type>> name(h, vector<type>(w));                               \
  in(name)
#define vvv(type, name, h, w, ...)                                             \
  vector<vector<vector<type>>> name(                                           \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
template <class T> auto max(const T &a) { return *max_element(all(a)); }
template <class T> auto min(const T &a) { return *min_element(all(a)); }
ll gcd(ll a, ll b) {
  while (b) {
    ll c = b;
    b = a % b;
    a = c;
  }
  return a;
}
ll lcm(ll a, ll b) {
  if (!a || !b)
    return 0;
  return a * b / gcd(a, b);
}
ll intpow(ll a, ll b) {
  ll ans = 1;
  while (b) {
    if (b & 1)
      ans *= a;
    a *= a;
    b /= 2;
  }
  return ans;
}
ll modpow(ll a, ll b, ll p) {
  ll ans = 1;
  while (b) {
    if (b & 1)
      (ans *= a) %= p;
    (a *= a) %= p;
    b /= 2;
  }
  return ans;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
vector<pll> factor(ull x) {
  vector<pll> ans;
  for (ll i = 2; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back({i, 1});
      while ((x /= i) % i == 0)
        ans.back().second++;
    }
  if (x != 1)
    ans.push_back({x, 1});
  return ans;
}
vector<ll> divisor(ull x) {
  vector<ll> ans;
  for (ll i = 1; i * i <= x; i++)
    if (x % i == 0)
      ans.push_back(i);
  rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]);
  return ans;
}
template <class T> unordered_map<T, ll> press(vector<T> &a) {
  auto b = a;
  sort(all(b));
  b.erase(unique(all(b)), b.end());
  unordered_map<T, ll> ans;
  rep(b.size()) ans[b[i]] = i;
  each(i, a) i = ans[i];
  return ans;
}
template <class T> map<T, ll> press_map(vector<T> &a) {
  auto b = a;
  sort(all(b));
  b.erase(unique(all(b)), b.end());
  map<T, ll> ans;
  rep(b.size()) ans[b[i]] = i;
  each(i, a) i = ans[i];
  return ans;
}
int scan() { return getchar(); }
void scan(int &a) { scanf("%d", &a); }
void scan(unsigned &a) { scanf("%u", &a); }
void scan(long &a) { scanf("%ld", &a); }
void scan(long long &a) { scanf("%lld", &a); }
void scan(unsigned long long &a) { scanf("%llu", &a); }
void scan(char &a) {
  do {
    a = getchar();
  } while (a == ' ' || a == '\n');
}
void scan(float &a) { scanf("%f", &a); }
void scan(double &a) { scanf("%lf", &a); }
void scan(long double &a) { scanf("%Lf", &a); }
void scan(vector<bool> &a) {
  for (unsigned i = 0; i < a.size(); i++) {
    int b;
    scan(b);
    a[i] = b;
  }
}
void scan(char a[]) { scanf("%s", a); }
void scan(string &a) { cin >> a; }
template <class T> void scan(vector<T> &);
template <class T, size_t size> void scan(array<T, size> &);
template <class T, class L> void scan(pair<T, L> &);
template <class T, size_t size> void scan(T (&)[size]);
template <class T> void scan(vector<T> &a) {
  for (auto &&i : a)
    scan(i);
}
template <class T> void scan(deque<T> &a) {
  for (auto &&i : a)
    scan(i);
}
template <class T, size_t size> void scan(array<T, size> &a) {
  for (auto &&i : a)
    scan(i);
}
template <class T, class L> void scan(pair<T, L> &p) {
  scan(p.first);
  scan(p.second);
}
template <class T, size_t size> void scan(T (&a)[size]) {
  for (auto &&i : a)
    scan(i);
}
template <class T> void scan(T &a) { cin >> a; }
void in() {}
template <class Head, class... Tail> void in(Head &head, Tail &...tail) {
  scan(head);
  in(tail...);
}
void print() { putchar(' '); }
void print(bool a) { printf("%d", a); }
void print(int a) { printf("%d", a); }
void print(unsigned a) { printf("%u", a); }
void print(long a) { printf("%ld", a); }
void print(long long a) { printf("%lld", a); }
void print(unsigned long long a) { printf("%llu", a); }
void print(char a) { printf("%c", a); }
void print(char a[]) { printf("%s", a); }
void print(const char a[]) { printf("%s", a); }
void print(float a) { printf("%.15f", a); }
void print(double a) { printf("%.15f", a); }
void print(long double a) { printf("%.15Lf", a); }
void print(const string &a) {
  for (auto &&i : a)
    print(i);
}
template <class T> void print(const vector<T> &);
template <class T, size_t size> void print(const array<T, size> &);
template <class T, class L> void print(const pair<T, L> &p);
template <class T, size_t size> void print(const T (&)[size]);
template <class T> void print(const vector<T> &a) {
  if (a.empty())
    return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    putchar(' ');
    print(*i);
  }
}
template <class T> void print(const deque<T> &a) {
  if (a.empty())
    return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    putchar(' ');
    print(*i);
  }
}
template <class T, size_t size> void print(const array<T, size> &a) {
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    putchar(' ');
    print(*i);
  }
}
template <class T, class L> void print(const pair<T, L> &p) {
  print(p.first);
  putchar(' ');
  print(p.second);
}
template <class T, size_t size> void print(const T (&a)[size]) {
  print(a[0]);
  for (auto i = a; ++i != end(a);) {
    putchar(' ');
    print(*i);
  }
}
template <class T> void print(const T &a) { cout << a; }
int out() {
  putchar('\n');
  return 0;
}
template <class T> int out(const T &t) {
  print(t);
  putchar('\n');
  return 0;
}
template <class Head, class... Tail>
int out(const Head &head, const Tail &...tail) {
  print(head);
  putchar(' ');
  out(tail...);
  return 0;
}
#ifdef DEBUG
void err() { putchar('\n'); }
template <class T> void err(const T &t) {
  print(t);
  putchar('\n');
}
template <class Head, class... Tail>
void err(const Head &head, const Tail &...tail) {
  print(head);
  putchar(' ');
  out(tail...);
}
#else
template <class... T> void err(const T &...) {}
#endif
int first(bool i = true) { return out(i ? "first" : "second"); }
int yes(bool i = true) { return out(i ? "yes" : "no"); }
int Yes(bool i = true) { return out(i ? "Yes" : "No"); }
int No() { return out("No"); }
int YES(bool i = true) { return out(i ? "YES" : "NO"); }
int NO() { return out("NO"); }
int Yay(bool i = true) { return out(i ? "Yay!" : ":("); }
int possible(bool i = true) { return out(i ? "possible" : "impossible"); }
int Possible(bool i = true) { return out(i ? "Possible" : "Impossible"); }
int POSSIBLE(bool i = true) { return out(i ? "POSSIBLE" : "IMPOSSIBLE"); }
void Case(ll i) { printf("Case #%lld: ", i); }

signed main() {
  LL(n);
  if (n == 1)
    return out("First");
  vec(vector<ll>, g, n);
  vec(ll, d, n);
  rep(n - 1) {
    LL(a, b);
    a--;
    b--;
    g[a].push_back(b);
    g[b].push_back(a);
    d[a]++;
    d[b]++;
  }
  ll root = 0;
  rep(n) if (d[i] == 1) root = i;
  vec(unordered_set<ll>, child, n);
  vec(ll, parent, n);
  auto dfs = [&](ll from, ll at, auto f) -> void {
    each(i, g[at]) if (i != from) {
      child[at].insert(i);
      parent[i] = at;
      f(at, i, f);
    }
  };
  dfs(-1, root, dfs);
  queue<ll> q;
  rep(n) q.push(i);
  vec(bool, deleted, n);
  while (q.size()) {
    ll at = q.front();
    q.pop();
    ll p, c;
    if (d[at] == 1 && at != root) {
      p = parent[at];
      c = at;
      if (d[p] < 1 || 2 < d[p])
        continue;
    }
    elif (d[at] == 2 || at == root) {
      p = at;
      if (child[at].empty())
        continue;
      c = *child[at].begin();
      if (d[c] != 1)
        continue;
    }
    else continue;
    if (deleted[p] || deleted[c])
      continue;
    each(i, g[p]) d[i]--;
    each(i, g[c]) d[i]--;
    child[parent[p]].erase(p);
    deleted[p] = deleted[c] = 1;
    q.push(parent[p]);
  }
  each(i, d) if (i) return out("First");
  out("Second");
}