#include <bits/stdc++.h>

#ifdef _MSC_VER
#  include <intrin.h>
#else
#  include <x86intrin.h>
#endif

#include <limits>
#include <type_traits>

namespace suisen {
// ! utility
template <typename ...Types>
using constraints_t = std::enable_if_t<std::conjunction_v<Types...>, std::nullptr_t>;
template <bool cond_v, typename Then, typename OrElse>
constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) {
    if constexpr (cond_v) {
        return std::forward<Then>(then);
    } else {
        return std::forward<OrElse>(or_else);
    }
}

// ! function
template <typename ReturnType, typename Callable, typename ...Args>
using is_same_as_invoke_result = std::is_same<std::invoke_result_t<Callable, Args...>, ReturnType>;
template <typename F, typename T>
using is_uni_op = is_same_as_invoke_result<T, F, T>;
template <typename F, typename T>
using is_bin_op = is_same_as_invoke_result<T, F, T, T>;

template <typename Comparator, typename T>
using is_comparator = std::is_same<std::invoke_result_t<Comparator, T, T>, bool>;

// ! integral
template <typename T, typename = constraints_t<std::is_integral<T>>>
constexpr int bit_num = std::numeric_limits<std::make_unsigned_t<T>>::digits;
template <typename T, unsigned int n>
struct is_nbit { static constexpr bool value = bit_num<T> == n; };
template <typename T, unsigned int n>
static constexpr bool is_nbit_v = is_nbit<T, n>::value;

// ?
template <typename T>
struct safely_multipliable {};
template <>
struct safely_multipliable<int> { using type = long long; };
template <>
struct safely_multipliable<long long> { using type = __int128_t; };
template <>
struct safely_multipliable<unsigned int> { using type = unsigned long long; };
template <>
struct safely_multipliable<unsigned long int> { using type = __uint128_t; };
template <>
struct safely_multipliable<unsigned long long> { using type = __uint128_t; };
template <>
struct safely_multipliable<float> { using type = float; };
template <>
struct safely_multipliable<double> { using type = double; };
template <>
struct safely_multipliable<long double> { using type = long double; };
template <typename T>
using safely_multipliable_t = typename safely_multipliable<T>::type;

template <typename T, typename = void>
struct rec_value_type {
    using type = T;
};
template <typename T>
struct rec_value_type<T, std::void_t<typename T::value_type>> {
    using type = typename rec_value_type<typename T::value_type>::type;
};
template <typename T>
using rec_value_type_t = typename rec_value_type<T>::type;

} // namespace suisen

// ! type aliases
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using pq_greater = std::priority_queue<T, std::vector<T>, std::greater<T>>;

// ! macros (internal)
#define DETAIL_OVERLOAD2(_1,_2,name,...) name
#define DETAIL_OVERLOAD3(_1,_2,_3,name,...) name
#define DETAIL_OVERLOAD4(_1,_2,_3,_4,name,...) name

#define DETAIL_REP4(i,l,r,s)  for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l);i<(r);i+=(s))
#define DETAIL_REP3(i,l,r)    DETAIL_REP4(i,l,r,1)
#define DETAIL_REP2(i,n)      DETAIL_REP3(i,0,n)
#define DETAIL_REPINF3(i,l,s) for(std::remove_reference_t<std::remove_const_t<decltype(l)>>i=(l);;i+=(s))
#define DETAIL_REPINF2(i,l)   DETAIL_REPINF3(i,l,1)
#define DETAIL_REPINF1(i)     DETAIL_REPINF2(i,0)
#define DETAIL_RREP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s))
#define DETAIL_RREP3(i,l,r)   DETAIL_RREP4(i,l,r,1)
#define DETAIL_RREP2(i,n)     DETAIL_RREP3(i,0,n)

#define DETAIL_CAT_I(a, b) a##b
#define DETAIL_CAT(a, b) DETAIL_CAT_I(a, b)
#define DETAIL_UNIQVAR(tag) DETAIL_CAT(tag, __LINE__)

// ! macros
#define REP(...)    DETAIL_OVERLOAD4(__VA_ARGS__, DETAIL_REP4   , DETAIL_REP3   , DETAIL_REP2   )(__VA_ARGS__)
#define RREP(...)   DETAIL_OVERLOAD4(__VA_ARGS__, DETAIL_RREP4  , DETAIL_RREP3  , DETAIL_RREP2  )(__VA_ARGS__)
#define REPINF(...) DETAIL_OVERLOAD3(__VA_ARGS__, DETAIL_REPINF3, DETAIL_REPINF2, DETAIL_REPINF1)(__VA_ARGS__)

#define LOOP(n) for (std::remove_reference_t<std::remove_const_t<decltype(n)>> DETAIL_UNIQVAR(loop_variable) = n; DETAIL_UNIQVAR(loop_variable) --> 0;)

#define ALL(iterable) std::begin(iterable), std::end(iterable)
#define INPUT(type, ...) type __VA_ARGS__; read(__VA_ARGS__)

// ! debug

#ifdef LOCAL
#  define debug(...) debug_internal(#__VA_ARGS__, __VA_ARGS__)

template <class T, class... Args>
void debug_internal(const char* s, T&& first, Args&&... args) {
    constexpr const char* prefix = "[\033[32mDEBUG\033[m] ";
    constexpr const char* open_brakets = sizeof...(args) == 0 ? "" : "(";
    constexpr const char* close_brakets = sizeof...(args) == 0 ? "" : ")";
    std::cerr << prefix << open_brakets << s << close_brakets << ": " << open_brakets << std::forward<T>(first);
    ((std::cerr << ", " << std::forward<Args>(args)), ...);
    std::cerr << close_brakets << "\n";
}

#else
#  define debug(...) void(0)
#endif

// ! I/O utilities

// __int128_t
std::ostream& operator<<(std::ostream& dest, __int128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
        __uint128_t tmp = value < 0 ? -value : value;
        char buffer[128];
        char* d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[tmp % 10];
            tmp /= 10;
        } while (tmp != 0);
        if (value < 0) {
            --d;
            *d = '-';
        }
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(std::ios_base::badbit);
        }
    }
    return dest;
}
// __uint128_t
std::ostream& operator<<(std::ostream& dest, __uint128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
        char buffer[128];
        char* d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[value % 10];
            value /= 10;
        } while (value != 0);
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(std::ios_base::badbit);
        }
    }
    return dest;
}

// pair
template <typename T, typename U>
std::ostream& operator<<(std::ostream& out, const std::pair<T, U>& a) {
    return out << a.first << ' ' << a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::ostream& operator<<(std::ostream& out, const std::tuple<Args...>& a) {
    if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) return out;
    else {
        out << std::get<N>(a);
        if constexpr (N + 1 < std::tuple_size_v<std::tuple<Args...>>) out << ' ';
        return operator<<<N + 1>(out, a);
    }
}
// vector
template <typename T>
std::ostream& operator<<(std::ostream& out, const std::vector<T>& a) {
    for (auto it = a.begin(); it != a.end();) {
        out << *it;
        if (++it != a.end()) out << ' ';
    }
    return out;
}
// array
template <typename T, size_t N>
std::ostream& operator<<(std::ostream& out, const std::array<T, N>& a) {
    for (auto it = a.begin(); it != a.end();) {
        out << *it;
        if (++it != a.end()) out << ' ';
    }
    return out;
}
inline void print() { std::cout << '\n'; }
template <typename Head, typename... Tail>
inline void print(const Head& head, const Tail &...tails) {
    std::cout << head;
    if (sizeof...(tails)) std::cout << ' ';
    print(tails...);
}
template <typename Iterable>
auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) {
    for (auto it = v.begin(); it != v.end();) {
        std::cout << *it;
        if (++it != v.end()) std::cout << sep;
    }
    std::cout << end;
}

__int128_t stoi128(const std::string& s) {
    __int128_t ret = 0;
    for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0';
    if (s[0] == '-') ret = -ret;
    return ret;
}
__uint128_t stou128(const std::string& s) {
    __uint128_t ret = 0;
    for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0';
    return ret;
}
// __int128_t
std::istream& operator>>(std::istream& in, __int128_t& v) {
    std::string s;
    in >> s;
    v = stoi128(s);
    return in;
}
// __uint128_t
std::istream& operator>>(std::istream& in, __uint128_t& v) {
    std::string s;
    in >> s;
    v = stou128(s);
    return in;
}
// pair
template <typename T, typename U>
std::istream& operator>>(std::istream& in, std::pair<T, U>& a) {
    return in >> a.first >> a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::istream& operator>>(std::istream& in, std::tuple<Args...>& a) {
    if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) return in;
    else return operator>><N + 1>(in >> std::get<N>(a), a);
}
// vector
template <typename T>
std::istream& operator>>(std::istream& in, std::vector<T>& a) {
    for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
    return in;
}
// array
template <typename T, size_t N>
std::istream& operator>>(std::istream& in, std::array<T, N>& a) {
    for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
    return in;
}
template <typename ...Args>
void read(Args &...args) {
    (std::cin >> ... >> args);
}

// ! integral utilities

// Returns pow(-1, n)
template <typename T> constexpr inline int pow_m1(T n) {
    return -(n & 1) | 1;
}
// Returns pow(-1, n)
template <> constexpr inline int pow_m1<bool>(bool n) {
    return -int(n) | 1;
}

// Returns floor(x / y)
template <typename T> constexpr inline T fld(const T x, const T y) {
    return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y;
}
template <typename T> constexpr inline T cld(const T x, const T y) {
    return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y;
}

template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u32(x); }
template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u64(x); }
template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }
template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num<T>; }
template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }
template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num<T>; }
template <typename T> constexpr inline int floor_log2(const T x) { return suisen::bit_num<T> - 1 - count_lz(x); }
template <typename T> constexpr inline int ceil_log2(const T x) { return floor_log2(x) + ((x & -x) != x); }
template <typename T> constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; }
template <typename T> constexpr inline int parity(const T x) { return popcount(x) & 1; }

// ! container

template <typename T, typename Comparator>
auto priqueue_comp(const Comparator comparator) {
    return std::priority_queue<T, std::vector<T>, Comparator>(comparator);
}

template <typename Container>
void sort_unique_erase(Container& a) {
    std::sort(a.begin(), a.end());
    a.erase(std::unique(a.begin(), a.end()), a.end());
}

template <typename InputIterator, typename BiConsumer>
auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) {
    if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr);
}
template <typename Container, typename BiConsumer>
auto foreach_adjacent_values(Container &&c, BiConsumer f) -> decltype(c.begin(), c.end(), void()) {
    foreach_adjacent_values(c.begin(), c.end(), f);
}

// ! other utilities

// x <- min(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmin(T& x, const T& y) {
    return y >= x ? false : (x = y, true);
}
// x <- max(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmax(T& x, const T& y) {
    return y <= x ? false : (x = y, true);
}

template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::string bin(T val, int bit_num = -1) {
    std::string res;
    if (bit_num != -1) {
        for (int bit = bit_num; bit-- > 0;) res += '0' + ((val >> bit) & 1);
    } else {
        for (; val; val >>= 1) res += '0' + (val & 1);
        std::reverse(res.begin(), res.end());
    }
    return res;
}

template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::vector<T> digits_low_to_high(T val, T base = 10) {
    std::vector<T> res;
    for (; val; val /= base) res.push_back(val % base);
    if (res.empty()) res.push_back(T{ 0 });
    return res;
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::vector<T> digits_high_to_low(T val, T base = 10) {
    auto res = digits_low_to_high(val, base);
    std::reverse(res.begin(), res.end());
    return res;
}

template <typename T>
std::string join(const std::vector<T>& v, const std::string& sep, const std::string& end) {
    std::ostringstream ss;
    for (auto it = v.begin(); it != v.end();) {
        ss << *it;
        if (++it != v.end()) ss << sep;
    }
    ss << end;
    return ss.str();
}

template <typename Func, typename Seq>
auto transform_to_vector(const Func &f, const Seq &s) {
    std::vector<std::invoke_result_t<Func, typename Seq::value_type>> v;
    v.reserve(std::size(s)), std::transform(std::begin(s), std::end(s), std::back_inserter(v), f);
    return v;
}
template <typename T, typename Seq>
auto copy_to_vector(const Seq &s) {
    std::vector<T> v;
    v.reserve(std::size(s)), std::copy(std::begin(s), std::end(s), std::back_inserter(v));
    return v;
}
template <typename Seq>
Seq concat(Seq s, const Seq &t) {
    s.reserve(std::size(s) + std::size(t));
    std::copy(std::begin(t), std::end(t), std::back_inserter(s));
    return s;
}
template <typename Seq>
std::vector<Seq> split(const Seq s, typename Seq::value_type delim) {
    std::vector<Seq> res;
    for (auto itl = std::begin(s), itr = itl;; itl = ++itr) {
        while (itr != std::end(s) and *itr != delim) ++itr;
        res.emplace_back(itl, itr);
        if (itr == std::end(s)) return res;
    }
}

int digit_to_int(char c) { return c - '0'; }
int lowercase_to_int(char c) { return c - 'a'; }
int uppercase_to_int(char c) { return c - 'A'; }

std::vector<int> digit_str_to_ints(const std::string &s) {
    return transform_to_vector(digit_to_int, s);
}
std::vector<int> lowercase_str_to_ints(const std::string &s) {
    return transform_to_vector(lowercase_to_int, s);
}
std::vector<int> uppercase_str_to_ints(const std::string &s) {
    return transform_to_vector(uppercase_to_int, s);
}

const std::string Yes = "Yes", No = "No", YES = "YES", NO = "NO";

namespace suisen {}
using namespace suisen;
using namespace std;

struct io_setup {
    io_setup(int precision = 20) {
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
        std::cout << std::fixed << std::setprecision(precision);
    }
} io_setup_ {};

// ! code from here

#include <algorithm>
#include <cassert>
#include <cstdint>
#include <optional>
#include <string>
#include <random>
#include <tuple>
#include <vector>
#include <utility>

namespace suisen::internal::implicit_treap {
    template <typename T, typename Derived>
    struct Node {
        using random_engine = std::mt19937;
        static inline random_engine rng{ std::random_device{}() };

        using priority_type = std::invoke_result_t<random_engine>;

        static priority_type random_priority() { return rng(); }

        using node_type = Derived;
        using node_pointer = uint32_t;

        using size_type = uint32_t;

        using difference_type = int32_t;
        using value_type = T;
        using pointer = value_type*;
        using const_pointer = const value_type*;
        using reference = value_type&;
        using const_reference = const value_type&;

        static inline std::vector<node_type> _nodes{};
        static inline std::vector<node_pointer> _erased{};

        static constexpr node_pointer null = ~node_pointer(0);

        node_pointer _ch[2]{ null, null };
        value_type _val;
        size_type _size;
        priority_type _priority;

        node_pointer _prev = null, _next = null;

        Node(const value_type val = {}): _val(val), _size(1), _priority(random_priority()) {}

        static void reserve(size_type capacity) { _nodes.reserve(capacity); }

        static bool is_null(node_pointer t) { return t == null; }
        static bool is_not_null(node_pointer t) { return not is_null(t); }

        static node_type& node(node_pointer t) { return _nodes[t]; }
        static const node_type& const_node(node_pointer t) { return _nodes[t]; }

        static value_type& value(node_pointer t) { return node(t)._val; }
        static value_type set_value(node_pointer t, const value_type& new_val) { return std::exchange(value(t), new_val); }

        static bool empty(node_pointer t) { return is_null(t); }
        static size_type& size(node_pointer t) { return node(t)._size; }
        static size_type safe_size(node_pointer t) { return empty(t) ? 0 : size(t); }

        static priority_type& priority(node_pointer t) { return node(t)._priority; }
        static void set_priority(node_pointer t, priority_type new_priority) { priority(t) = new_priority; }

        static node_pointer& prev(node_pointer t) { return node(t)._prev; }
        static node_pointer& next(node_pointer t) { return node(t)._next; }
        static void link(node_pointer l, node_pointer r) { next(l) = r, prev(r) = l; }

        static node_pointer min(node_pointer t) {
            while (true) {
                node_pointer nt = child0(t);
                if (is_null(nt)) return t;
                t = nt;
            }
        }
        static node_pointer max(node_pointer t) {
            while (true) {
                node_pointer nt = child1(t);
                if (is_null(nt)) return t;
                t = nt;
            }
        }

        static node_pointer& child0(node_pointer t) { return node(t)._ch[0]; }
        static node_pointer& child1(node_pointer t) { return node(t)._ch[1]; }
        static node_pointer& child(node_pointer t, bool b) { return node(t)._ch[b]; }
        static node_pointer set_child0(node_pointer t, node_pointer cid) { return std::exchange(child0(t), cid); }
        static node_pointer set_child1(node_pointer t, node_pointer cid) { return std::exchange(child1(t), cid); }
        static node_pointer set_child(node_pointer t, bool b, node_pointer cid) { return std::exchange(child(t, b), cid); }

        static node_pointer update(node_pointer t) { // t : not null
            size(t) = safe_size(child0(t)) + safe_size(child1(t)) + 1;
            return t;
        }

        static node_pointer empty_node() { return null; }
        template <typename ...Args>
        static node_pointer create_node(Args &&...args) {
            if (_erased.size()) {
                node_pointer res = _erased.back();
                _erased.pop_back();
                node(res) = node_type(std::forward<Args>(args)...);
                return res;
            } else {
                node_pointer res = _nodes.size();
                _nodes.emplace_back(std::forward<Args>(args)...);
                return res;
            }
        }
        static void delete_node(node_pointer t) { _erased.push_back(t); }
        static void delete_tree(node_pointer t) {
            if (is_null(t)) return;
            delete_tree(child0(t));
            delete_tree(child1(t));
            delete_node(t);
        }

        template <typename ...Args>
        static node_pointer build(Args &&... args) {
            std::vector<value_type> dat(std::forward<Args>(args)...);

            const size_t n = dat.size();

            std::vector<priority_type> priorities(n);
            std::generate(priorities.begin(), priorities.end(), random_priority);
            std::make_heap(priorities.begin(), priorities.end());

            std::vector<node_pointer> nodes(n);

            auto rec = [&](auto rec, size_t heap_index, size_t dat_index_offset) -> std::pair<size_t, node_pointer> {
                if (heap_index >= n) return { 0, null };
                auto [lsiz, lch] = rec(rec, 2 * heap_index + 1, dat_index_offset);
                dat_index_offset += lsiz;
                node_pointer root = create_node(std::move(dat[dat_index_offset]));
                nodes[dat_index_offset] = root;
                set_priority(root, priorities[heap_index]);
                if (dat_index_offset) {
                    link(nodes[dat_index_offset - 1], root);
                }
                dat_index_offset += 1;
                auto [rsiz, rch] = rec(rec, 2 * heap_index + 2, dat_index_offset);
                set_child0(root, lch);
                set_child1(root, rch);
                return { lsiz + 1 + rsiz, node_type::update(root) };
            };
            return rec(rec, 0, 0).second;
        }

        static std::pair<node_pointer, node_pointer> split(node_pointer t, size_type k) {
            if (k == 0) return { null, t };
            if (k == size(t)) return { t, null };

            static std::vector<node_pointer> lp{}, rp{};

            while (true) {
                if (const size_type lsiz = safe_size(child0(t)); k <= lsiz) {
                    if (rp.size()) set_child0(rp.back(), t);
                    rp.push_back(t);
                    if (k == lsiz) {
                        if (lp.size()) set_child1(lp.back(), child0(t));

                        node_pointer lt = set_child0(t, null), rt = null;

                        while (lp.size()) node_type::update(lt = lp.back()), lp.pop_back();
                        while (rp.size()) node_type::update(rt = rp.back()), rp.pop_back();

                        return { lt, rt };
                    }
                    t = child0(t);
                } else {
                    if (lp.size()) set_child1(lp.back(), t);
                    lp.push_back(t);
                    t = child1(t);
                    k -= lsiz + 1;
                }
            }
        }
        static std::tuple<node_pointer, node_pointer, node_pointer> split(node_pointer t, size_type l, size_type r) {
            auto [tlm, tr] = split(t, r);
            auto [tl, tm] = split(tlm, l);
            return { tl, tm, tr };
        }

        static node_pointer merge_impl(node_pointer tl, node_pointer tr) {
            if (priority(tl) < priority(tr)) {
                if (node_pointer tm = child0(tr); is_null(tm)) {
                    link(max(tl), tr);
                    set_child0(tr, tl);
                } else {
                    set_child0(tr, merge(tl, tm));
                }
                return node_type::update(tr);
            } else {
                if (node_pointer tm = child1(tl); is_null(tm)) {
                    link(tl, min(tr));
                    set_child1(tl, tr);
                } else {
                    set_child1(tl, merge(tm, tr));
                }
                return node_type::update(tl);
            }
        }
        static node_pointer merge(node_pointer tl, node_pointer tr) {
            if (is_null(tl)) return tr;
            if (is_null(tr)) return tl;
            return merge_impl(tl, tr);
        }
        static node_pointer merge(node_pointer tl, node_pointer tm, node_pointer tr) {
            return merge(merge(tl, tm), tr);
        }

        static node_pointer insert_impl(node_pointer t, size_type k, node_pointer new_node) {
            if (is_null(t)) return new_node;
            static std::vector<node_pointer> st;
            bool b = false;

            while (true) {
                if (is_null(t) or priority(new_node) > priority(t)) {
                    if (is_null(t)) {
                        t = new_node;
                    } else {
                        auto [tl, tr] = split(t, k);
                        if (is_not_null(tl)) link(max(tl), new_node);
                        if (is_not_null(tr)) link(new_node, min(tr));
                        set_child0(new_node, tl);
                        set_child1(new_node, tr);
                        t = node_type::update(new_node);
                    }
                    if (st.size()) {
                        set_child(st.back(), b, t);
                        do t = node_type::update(st.back()), st.pop_back(); while (st.size());
                    }
                    return t;
                } else {
                    if (const size_type lsiz = safe_size(child0(t)); k <= lsiz) {
                        if (k == lsiz) link(new_node, t);
                        st.push_back(t), b = false;
                        t = child0(t);
                    } else {
                        if (k == lsiz + 1) link(t, new_node);
                        st.push_back(t), b = true;
                        t = child1(t);
                        k -= lsiz + 1;
                    }
                }
            }
        }
        template <typename ...Args>
        static node_pointer insert(node_pointer t, size_type k, Args &&...args) {
            return insert_impl(t, k, create_node(std::forward<Args>(args)...));
        }

        static std::pair<node_pointer, value_type> erase(node_pointer t, size_type k) {
            if (const size_type lsiz = safe_size(child0(t)); k == lsiz) {
                delete_node(t);
                return { merge(child0(t), child1(t)), std::move(value(t)) };
            } else if (k < lsiz) {
                auto [c0, v] = erase(child0(t), k);
                set_child0(t, c0);
                if (is_not_null(c0) and k == lsiz - 1) link(max(c0), t);
                return { node_type::update(t), std::move(v) };
            } else {
                auto [c1, v] = erase(child1(t), k - (lsiz + 1));
                set_child1(t, c1);
                if (is_not_null(c1) and k == lsiz + 1) link(t, min(c1));
                return { node_type::update(t), std::move(v) };
            }
        }

        static node_pointer rotate(node_pointer t, size_type k) {
            auto [tl, tr] = split(t, k);
            return merge(tr, tl);
        }
        static node_pointer rotate(node_pointer t, size_type l, size_type m, size_type r) {
            auto [tl, tm, tr] = split(t, l, r);
            return merge(tl, rotate(tm, m - l), tr);
        }

        template <typename Func>
        static node_pointer set_update(node_pointer t, size_type k, const Func& f) {
            if (const size_type lsiz = safe_size(child0(t)); k == lsiz) {
                value_type& val = value(t);
                val = f(const_cast<const value_type&>(val));
            } else if (k < lsiz) {
                set_child0(t, set_update(child0(t), k, f));
            } else {
                set_child1(t, set_update(child1(t), k - (lsiz + 1), f));
            }
            return node_type::update(t);
        }

        static std::vector<value_type> dump(node_pointer t) {
            std::vector<value_type> res;
            res.reserve(safe_size(t));
            auto rec = [&](auto rec, node_pointer t) -> void {
                if (is_null(t)) return;
                rec(rec, child0(t));
                res.push_back(value(t));
                rec(rec, child1(t));
            };
            rec(rec, t);
            return res;
        }

        template <bool reversed_, bool constant_>
        struct NodeIterator {
            static constexpr bool constant = constant_;
            static constexpr bool reversed = reversed_;

            friend Node;
            friend Derived;

            using difference_type = Node::difference_type;
            using value_type = Node::value_type;
            using pointer = std::conditional_t<constant, Node::const_pointer, Node::pointer>;
            using reference = std::conditional_t<constant, Node::const_reference, Node::reference>;
            using iterator_category = std::random_access_iterator_tag;

            NodeIterator(): NodeIterator(null) {}
            explicit NodeIterator(node_pointer root): NodeIterator(root, 0, null) {}
            NodeIterator(const NodeIterator<reversed, not constant>& it): NodeIterator(it._root, it._index, it._cur) {}

            reference operator*() const {
                if (is_null(_cur) and _index != safe_size(_root)) {
                    _cur = _root;
                    for (size_type k = _index;;) {
                        if (size_type siz = safe_size(child(_cur, reversed)); k == siz) {
                            break;
                        } else if (k < siz) {
                            _cur = child(_cur, reversed);
                        } else {
                            _cur = child(_cur, not reversed);
                            k -= siz + 1;
                        }
                    }
                }
                return value(_cur);
            }
            reference operator[](difference_type k) const { return *((*this) + k); }

            NodeIterator& operator++() { return *this += 1; }
            NodeIterator& operator--() { return *this -= 1; }
            NodeIterator& operator+=(difference_type k) { return suc(+k), * this; }
            NodeIterator& operator-=(difference_type k) { return suc(-k), * this; }
            NodeIterator operator++(int) { NodeIterator res = *this; ++(*this); return res; }
            NodeIterator operator--(int) { NodeIterator res = *this; --(*this); return res; }
            friend NodeIterator operator+(NodeIterator it, difference_type k) { return it += k; }
            friend NodeIterator operator+(difference_type k, NodeIterator it) { return it += k; }
            friend NodeIterator operator-(NodeIterator it, difference_type k) { return it -= k; }

            friend difference_type operator-(const NodeIterator& lhs, const NodeIterator& rhs) { return lhs._index - rhs._index; }

            friend bool operator==(const NodeIterator& lhs, const NodeIterator& rhs) { return lhs._index == rhs._index; }
            friend bool operator!=(const NodeIterator& lhs, const NodeIterator& rhs) { return lhs._index != rhs._index; }
            friend bool operator<(const NodeIterator& lhs, const NodeIterator& rhs) { return lhs._index < rhs._index; }
            friend bool operator>(const NodeIterator& lhs, const NodeIterator& rhs) { return lhs._index > rhs._index; }
            friend bool operator<=(const NodeIterator& lhs, const NodeIterator& rhs) { return lhs._index <= rhs._index; }
            friend bool operator>=(const NodeIterator& lhs, const NodeIterator& rhs) { return lhs._index >= rhs._index; }

            static NodeIterator begin(node_pointer root) { return NodeIterator(root, 0, null); }
            static NodeIterator end(node_pointer root) { return NodeIterator(root, safe_size(root), null); }

            int size() const { return safe_size(_root); }
            int index() const { return _index; }
        private:
            node_pointer _root;
            size_type _index;
            mutable node_pointer _cur; // it==end() or uninitialized (updates only index)

            NodeIterator(node_pointer root, size_type index, node_pointer cur): _root(root), _index(index), _cur(cur) {}

            void suc(difference_type k) {
                _index += k;
                if (_index == safe_size(_root) or std::abs(k) >= 20) _cur = null;
                if (is_null(_cur)) return;

                const bool positive = k < 0 ? (k = -k, reversed) : not reversed;

                if (positive) {
                    while (k-- > 0) _cur = next(_cur);
                } else {
                    while (k-- > 0) _cur = prev(_cur);
                }
            }

            node_pointer root() const { return _root; }
            void set_root(node_pointer new_root, size_type new_index) { _root = new_root, _index = new_index; }

            node_pointer get_child0() const { return child0(_cur); }
            node_pointer get_child1() const { return child1(_cur); }

            template <typename Predicate>
            static NodeIterator binary_search(node_pointer t, const Predicate& f) {
                NodeIterator res(t, safe_size(t), null);
                if (is_null(t)) return res;

                NodeIterator it(t, safe_size(child0(t)), t);
                while (is_not_null(it._cur)) {
                    if (f(it)) {
                        res = it;
                        it._cur = it.get_child0();
                        it._index -= is_null(it._cur) ? 1 : safe_size(it.get_child1()) + 1;
                    } else {
                        it._cur = it.get_child1();
                        it._index += is_null(it._cur) ? 1 : safe_size(it.get_child0()) + 1;
                    }
                }
                return res;
            }

            size_type get_gap_index_left() const {
                if constexpr (reversed) return size() - index();
                else return index();
            }
            size_type get_element_index_left() const {
                if constexpr (reversed) return size() - index() - 1;
                else return index();
            }
        };
        using iterator = NodeIterator<false, false>;
        using reverse_iterator = NodeIterator<true, false>;
        using const_iterator = NodeIterator<false, true>;
        using const_reverse_iterator = NodeIterator<true, true>;

        template <typename>
        struct is_node_iterator: std::false_type {};
        template <bool reversed_, bool constant_>
        struct is_node_iterator<NodeIterator<reversed_, constant_>>: std::true_type {};
        template <typename X>
        static constexpr bool is_node_iterator_v = is_node_iterator<X>::value;

        static iterator begin(node_pointer t) { return iterator::begin(t); }
        static iterator end(node_pointer t) { return iterator::end(t); }
        static reverse_iterator rbegin(node_pointer t) { return reverse_iterator::begin(t); }
        static reverse_iterator rend(node_pointer t) { return reverse_iterator::end(t); }
        static const_iterator cbegin(node_pointer t) { return const_iterator::begin(t); }
        static const_iterator cend(node_pointer t) { return const_iterator::end(t); }
        static const_reverse_iterator crbegin(node_pointer t) { return const_reverse_iterator::begin(t); }
        static const_reverse_iterator crend(node_pointer t) { return const_reverse_iterator::end(t); }

        // Find the first element that satisfies the condition f : iterator -> { false, true }.
        // Returns const_iterator
        template <typename Iterator, typename Predicate, std::enable_if_t<is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
        static Iterator binary_search(node_pointer t, const Predicate& f) {
            return Iterator::binary_search(t, f);
        }
        // comp(T t, U u) = (t < u)
        template <typename Iterator, typename U, typename Compare = std::less<>, std::enable_if_t<is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
        static Iterator lower_bound(node_pointer t, const U& target, Compare comp) {
            return binary_search<Iterator>(t, [&](Iterator it) { return not comp(*it, target); });
        }
        // comp(T u, U t) = (u < t)
        template <typename Iterator, typename U, typename Compare = std::less<>, std::enable_if_t<is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
        static Iterator upper_bound(node_pointer t, const U& target, Compare comp) {
            return binary_search<Iterator>(t, [&](Iterator it) { return comp(target, *it); });
        }

        template <typename Iterator, std::enable_if_t<is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
        static node_pointer insert(Iterator it, const value_type& val) {
            return insert(it.root(), it.get_gap_index_left(), val);
        }
        template <typename Iterator, std::enable_if_t<is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
        static std::pair<node_pointer, value_type> erase(Iterator it) {
            return erase(it.root(), it.get_element_index_left());
        }
        template <typename Iterator, std::enable_if_t<is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
        static std::pair<node_pointer, node_pointer> split(Iterator it) {
            return split(it.root(), it.get_gap_index_left());
        }
    };
} // namespace suisen::internal::implicit_treap

namespace suisen {
    namespace internal::implicit_treap {
        template <typename T>
        struct DefaultNode: Node<T, DefaultNode<T>> {
            using base = Node<T, DefaultNode<T>>;
            using base::base;
        };
    }

    template <typename T>
    class DynamicArray {
        using node_type = internal::implicit_treap::DefaultNode<T>;
        using node_pointer = typename node_type::node_pointer;

        node_pointer _root;

        struct node_pointer_construct {};
        DynamicArray(node_pointer root, node_pointer_construct): _root(root) {}

    public:
        using value_type = typename node_type::value_type;

        DynamicArray(): _root(node_type::empty_node()) {}
        explicit DynamicArray(size_t n, const value_type& fill_value = {}): _root(node_type::build(n, fill_value)) {}
        template <typename U>
        DynamicArray(const std::vector<U>& dat) : _root(node_type::build(dat.begin(), dat.end())) {}

        void free() {
            node_type::delete_tree(_root);
            _root = node_type::empty_node();
        }
        void clear() { free(); }

        static void reserve(size_t capacity) { node_type::reserve(capacity); }

        bool empty() const { return node_type::empty(_root); }
        int size() const { return node_type::safe_size(_root); }

        value_type& operator[](size_t k) {
            assert(k < size_t(size()));
            return begin()[k];
        }
        const value_type& operator[](size_t k) const {
            assert(k < size_t(size()));
            return cbegin()[k];
        }
        value_type& front() { return *begin(); }
        value_type& back() { return *rbegin(); }
        const value_type& front() const { return *cbegin(); }
        const value_type& back() const { return *crbegin(); }

        void insert(size_t k, const value_type& val) {
            assert(k <= size_t(size()));
            _root = node_type::insert(_root, k, val);
        }
        void push_front(const value_type& val) { insert(0, val); }
        void push_back(const value_type& val) { insert(size(), val); }

        value_type erase(size_t k) {
            assert(k <= size_t(size()));
            value_type v;
            std::tie(_root, v) = node_type::erase(_root, k);
            return v;
        }
        value_type pop_front() { return erase(0); }
        value_type pop_back() { return erase(size() - 1); }

        // Split immediately before the k-th element.
        DynamicArray split(size_t k) {
            assert(k <= size_t(size()));
            node_pointer root_r;
            std::tie(_root, root_r) = node_type::split(_root, k);
            return DynamicArray(root_r, node_pointer_construct{});
        }

        void merge(DynamicArray r) { _root = node_type::merge(_root, r._root); }

        void rotate(size_t k) {
            assert(k <= size_t(size()));
            _root = node_type::rotate(_root, k);
        }
        void rotate(size_t l, size_t m, size_t r) {
            assert(l <= m and m <= r and r <= size_t(size()));
            _root = node_type::rotate(_root, l, m, r);
        }

        std::vector<value_type> dump() const { return node_type::dump(_root); }

        using iterator = typename node_type::iterator;
        using reverse_iterator = typename node_type::reverse_iterator;
        using const_iterator = typename node_type::const_iterator;
        using const_reverse_iterator = typename node_type::const_reverse_iterator;

        iterator begin() { return node_type::begin(_root); }
        iterator end() { return node_type::end(_root); }
        reverse_iterator rbegin() { return node_type::rbegin(_root); }
        reverse_iterator rend() { return node_type::rend(_root); }

        const_iterator begin() const { return cbegin(); }
        const_iterator end() const { return cend(); }
        const_reverse_iterator rbegin() const { return crbegin(); }
        const_reverse_iterator rend() const { return crend(); }
        const_iterator cbegin() const { return node_type::cbegin(_root); }
        const_iterator cend() const { return node_type::cend(_root); }
        const_reverse_iterator crbegin() const { return node_type::crbegin(_root); }
        const_reverse_iterator crend() const { return node_type::crend(_root); }

        // Find the first element that satisfies the condition f.
        // Returns { position, optional(value) }
        // Requirements: f(A[i]) must be monotonic
        template <typename Predicate>
        iterator binary_search(const Predicate& f) {
            return node_type::template binary_search<iterator>(_root, f);
        }
        // comp(T t, U u) = (t < u)
        // Requirements: sequence is sorted
        template <typename U, typename Compare = std::less<>>
        iterator lower_bound(const U& target, Compare comp = {}) {
            return node_type::template lower_bound<iterator>(_root, target, comp);
        }
        // comp(T u, U t) = (u < t)
        // Requirements: sequence is sorted
        template <typename U, typename Compare = std::less<>>
        iterator upper_bound(const U& target, Compare comp = {}) {
            return node_type::template upper_bound<iterator>(_root, target, comp);
        }
        // Find the first element that satisfies the condition f.
        // Returns { position, optional(value) }
        // Requirements: f(A[i]) must be monotonic
        template <typename Predicate>
        const_iterator binary_search(const Predicate& f) const {
            return node_type::template binary_search<const_iterator>(_root, f);
        }
        // comp(T t, U u) = (t < u)
        // Requirements: sequence is sorted
        template <typename U, typename Compare = std::less<>>
        const_iterator lower_bound(const U& target, Compare comp = {}) const {
            return node_type::template lower_bound<const_iterator>(_root, target, comp);
        }
        // comp(T u, U t) = (u < t)
        // Requirements: sequence is sorted
        template <typename U, typename Compare = std::less<>>
        const_iterator upper_bound(const U& target, Compare comp = {}) const {
            return node_type::template upper_bound<const_iterator>(_root, target, comp);
        }
 
        template <typename Iterator, std::enable_if_t<node_type::template is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
        void insert(Iterator it, const value_type &val) {
            _root = node_type::insert(it, val);
        }
        template <typename Iterator, std::enable_if_t<node_type::template is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
        value_type erase(Iterator it) {
            value_type erased;
            std::tie(_root, erased) = node_type::erase(it);
            return erased;
        }
        template <typename Iterator, std::enable_if_t<node_type::template is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
        DynamicArray split(Iterator it) {
            node_pointer root_r;
            std::tie(_root, root_r) = node_type::split(it);
            return DynamicArray(root_r, node_pointer_construct{});
        }

        // handling internal nodes
        using internal_node = node_type;
        using internal_node_pointer = node_pointer;

        internal_node_pointer& root_node() { return _root; }
        const internal_node_pointer& root_node() const { return _root; }
        void set_root_node(internal_node_pointer new_root) { root_node() = new_root; }
    };
} // namespace suisen

bool ops[4][2][2] {
    {
        { 0, 0 },
        { 0, 1 }
    },
    {
        { 0, 1 },
        { 1, 1 },
    },
    {
        { 0, 1 },
        { 1, 0 }
    },
    {
        { 1, 1 },
        { 0, 1 }
    }
};

array<char, 256> op;

void solve() {
    op['a'] = 0;
    op['o'] = 1;
    op['x'] = 2;
    op['i'] = 3;

    int n;
    read(n);

    vector<bool> init_a(n);
    vector<int> init_y(n - 1);
    REP(i, n) {
        string s;
        read(s);
        init_a[i] = s == "True";
    }
    REP(i, n - 1) {
        string s;
        read(s);
        init_y[i] = op[s.front()];
    }
    DynamicArray<bool> a(init_a);
    DynamicArray<int> y(init_y);

    LOOP(n - 1) {
        // debug(a.dump());
        // debug(y.dump());

        int pos;
        read(pos);
        --pos;
        a[pos] = ops[y[pos]][a[pos]][a[pos + 1]];
        y.erase(pos);
        a.erase(pos + 1);
    }
    print(a.front() ? "True" : "False");
}

int main() {
    int t;
    read(t);
    LOOP(t) {
        solve();
    }
    return 0;
}