#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif int mex(const vector &v) { const int N = v.size(); vector mex(N + 1); for (int x : v) { if (x < N) mex.at(x) = 1; } REP(i, N + 1) { if (!mex.at(i)) return i; } assert(false); } int calc_grundy(const vector &par) { const int N = par.size(); vector grundy(1 << N, -1); grundy.at(1) = 0; FOR(S, 2, 1 << N) { bool bad = false; int is_leaf = S; REP(i, N) { if (!((S >> i) & 1)) continue; const int p = par.at(i); if (p == -1) continue; if (!((S >> p) & 1)) bad = true; is_leaf &= ~(1 << p); } if (bad) continue; // vector gs; int gsmask = 0; for (int leaf = is_leaf; leaf; leaf = (leaf - 1) & is_leaf) { gsmask |= 1 << grundy.at(S ^ leaf); // gs.push_back(grundy.at(S ^ leaf)); } int g = 0; while (gsmask & (1 << g)) ++g; grundy.at(S) = g; // grundy.at(S) = mex(gs); } return grundy.back(); } struct rand_int_ { using lint = long long; std::mt19937 mt; rand_int_() : mt(std::chrono::steady_clock::now().time_since_epoch().count()) {} lint operator()(lint x) { return this->operator()(0, x); } // [0, x) lint operator()(lint l, lint r) { std::uniform_int_distribution d(l, r - 1); return d(mt); } } rnd; int main() { for (long long ntry = 1;; ntry++) { break; int n = rnd(6, 20); vector par(n, -1); par.at(1) = 0; FOR(i, 2, n) { par.at(i) = rnd(1, i); } if (calc_grundy(par) == 0) { dbg(par); } if (__builtin_popcountll(ntry) == 1) { dbg(ntry); // dbg(par); } } int T; cin >> T; while (T--) { int N; cin >> N; vector> child(N); vector par(N, -1); FOR(i, 1, N) { int p; cin >> p; --p; par.at(i) = p; child.at(p).push_back(i); } // // isP[v] = 「v の部分木ゲームで、させない方が負けのルールで、後手が勝てるか?」 // // isN[v] = 「v の部分木ゲームで、させない方が勝ちのルールで、後手が勝てるか?」 // vector isP(N), isN(N); // auto rec = [&](auto &&self, int now) -> void { // if (child.at(now).empty()) { // isP.at(now) = 1; // return; // } // for (int nxt : child.at(now)) { // self(self, nxt); // } // isP.at(now) = 1; // isN.at(now) = 1; // for (int nxt : child.at(now)) { // if (!isN.at(nxt)) isP.at(now) = 0; // if (!isP.at(nxt)) isN.at(now) = 0; // } // }; // rec(rec, 0); // dbg(isP); // dbg(isN); auto check = [&](int x) -> bool { if (child.at(x).empty()) return false; int depth = 1; while (child.at(x).size() == 1) { ++depth; x = child.at(x).front(); } if (child.at(x).empty()) return depth % 2 == 0; bool res = true; auto rec = [&](auto &&self, int now, bool sgn) -> void { for (int nxt : child.at(now)) { self(self, nxt, !sgn); } if (child.at(now).size() != 1 and sgn) res = false; }; rec(rec, x, false); return res; }; bool is_p = true; for (int c : child.at(0)) { if (!check(c)) { dbg(c); is_p = false; break; } } // auto g = calc_grundy(par); cout << (is_p ? "Second" : "First") << '\n'; } }