#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);
}

template <typename T, typename ToKey, typename CompareValue = std::less<>,
    std::enable_if_t<
        std::conjunction_v<
            std::is_invocable<ToKey, T>,
            std::is_invocable_r<bool, CompareValue, std::invoke_result_t<ToKey, T>, std::invoke_result_t<ToKey, T>
        >
    >, std::nullptr_t> = nullptr
>
auto comparator(const ToKey &to_key, const CompareValue &compare_value = std::less<>()) {
    return [to_key, compare_value](const T& x, const T& y) { return compare_value(to_key(x), to_key(y)); };
}

template <typename ToKey, std::enable_if_t<std::is_invocable_v<ToKey, int>, std::nullptr_t> = nullptr>
std::vector<int> sorted_indices(int n, const ToKey &to_key) {
    std::vector<int> p(n);
    std::iota(p.begin(), p.end(), 0);
    std::sort(p.begin(), p.end(), comparator<int>(to_key));
    return p;
}
template <typename Compare, std::enable_if_t<std::is_invocable_r_v<bool, Compare, int, int>, std::nullptr_t> = nullptr>
std::vector<int> sorted_indices(int n, const Compare &compare) {
    std::vector<int> p(n);
    std::iota(p.begin(), p.end(), 0);
    std::sort(p.begin(), p.end(), compare);
    return p;
}

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 <utility>
#include <vector>

// l <= x < r
template <typename T>
constexpr inline bool in_range(const T &x, const T &l, const T &r) {
    return l <= x and x < r;
}
// 0 <= x < r
template <typename T>
constexpr inline bool in_range(const T &x, const T &r) {
    return (std::make_unsigned_t<T>) x < (std::make_unsigned_t<T>) r;
}
// not (l <= x < r)
template <typename T>
constexpr inline bool out_range(const T &x, const T &l, const T &r) {
    return x < l or r <= x;
}
// not (0 <= x < r)
template <typename T>
constexpr inline bool out_range(const T &x, const T &r) {
    return (std::make_unsigned_t<T>) x >= (std::make_unsigned_t<T>) r;
}

constexpr int dx4[4] = {1, 0, -1, 0};
constexpr int dy4[4] = {0, 1, 0, -1};
constexpr int dx8[8] = {1, 1, 0, -1, -1, -1, 0, 1};
constexpr int dy8[8] = {0, 1, 1, 1, 0, -1, -1, -1};

constexpr std::pair<int, int> dxy4[4] = {
    { dx4[0], dy4[0] }, { dx4[1], dy4[1] }, { dx4[2], dy4[2] }, { dx4[3], dy4[3] },
};
constexpr std::pair<int, int> dxy8[8] = {
    { dx8[0], dy8[0] }, { dx8[1], dy8[1] }, { dx8[2], dy8[2] }, { dx8[3], dy8[3] },
    { dx8[4], dy8[4] }, { dx8[5], dy8[5] }, { dx8[6], dy8[6] }, { dx8[7], dy8[7] },
};

template <int D, auto dx, auto dy>
struct AdjacentCells {
    struct Iterator {
        const int x, y;
        int d;
        bool operator!=(std::nullptr_t) { return d != D; }
        void operator++() { ++d; }
        std::pair<int, int> operator*() { return { x + dx[d], y + dy[d] }; }
    };
    const int x, y;
    AdjacentCells(int x, int y) : x(x), y(y) {}
    auto begin() { return Iterator { x, y, 0 }; }
    constexpr std::nullptr_t end() { return nullptr; }
    operator std::vector<std::pair<int, int>>() {
        std::vector<std::pair<int, int>> res;
        for (const auto &p : *this) res.push_back(p);
        return res;
    }
};

template <int D, auto dx, auto dy>
struct AdjacentCellsBounded {
    struct Iterator {
        const int x, y, xl, xr, yl, yr;
        int d;
        bool operator!=(std::nullptr_t) {
            for (; d != D; ++d) if (in_range(x + dx[d], xl, xr) and in_range(y + dy[d], yl, yr)) return true;
            return false;
        }
        void operator++() { ++d; }
        std::pair<int, int> operator*() { return { x + dx[d], y + dy[d] }; }
    };
    const int x, y, xl, xr, yl, yr;
    AdjacentCellsBounded(int x, int y, int xl, int xr, int yl, int yr) : x(x), y(y), xl(xl), xr(xr), yl(yl), yr(yr) {}
    AdjacentCellsBounded(int x, int y, int xr, int yr) : AdjacentCellsBounded(x, y, 0, xr, 0, yr) {}
    auto begin() { return Iterator { x, y, xl, xr, yl, yr, 0 }; }
    constexpr std::nullptr_t end() { return nullptr; }
    operator std::vector<std::pair<int, int>>() {
        std::vector<std::pair<int, int>> res;
        for (const auto &p : *this) res.push_back(p);
        return res;
    }
};

// [ {x+dx4[i], y+dy4[i]} for i in range(4) ]
using AdjacentFourCells = AdjacentCells<4, dx4, dy4>;
// [ {nx:=x+dx4[i], ny:=y+dy4[i]} for i in range(4) if xl<=nx<xr and yl<=ny<yr ]
using AdjacentFourCellsBounded = AdjacentCellsBounded<4, dx4, dy4>;

// [ {x+dx8[i], y+dy8[i]} for i in range(8) ]
using AdjacentEightCells = AdjacentCells<8, dx8, dy8>;
// [ {nx:=x+dx8[i], ny:=y+dy8[i]} for i in range(8) if xl<=nx<xr and yl<=ny<yr ]
using AdjacentEightCellsBounded = AdjacentCellsBounded<8, dx8, dy8>;

// [ {x+dx4[i], y+dy4[i]} for i in range(4) ]
auto adjacent_four_cells(int x, int y) { return AdjacentFourCells { x, y }; }
// [ {nx:=x+dx4[i], ny:=y+dy4[i]} for i in range(4) if xl<=nx<xr and yl<=ny<yr ]
auto adjacent_four_cells(int x, int y, int xl, int xr, int yl, int yr) { return AdjacentFourCellsBounded { x, y, xl, xr, yl, yr }; }
// [ {nx:=x+dx4[i], ny:=y+dy4[i]} for i in range(4) if 0 <=nx<xr and 0 <=ny<yr ]
auto adjacent_four_cells(int x, int y,         int xr,         int yr) { return AdjacentFourCellsBounded { x, y, 0 , xr, 0 , yr }; }

// [ {x+dx8[i], y+dy8[i]} for i in range(8) ]
auto adjacent_eight_cells(int x, int y) { return AdjacentEightCells { x, y }; }
// [ {nx:=x+dx8[i], ny:=y+dy8[i]} for i in range(8) if xl<=nx<xr and yl<=ny<yr ]
auto adjacent_eight_cells(int x, int y, int xl, int xr, int yl, int yr) { return AdjacentEightCellsBounded { x, y, xl, xr, yl, yr }; }
// [ {nx:=x+dx8[i], ny:=y+dy8[i]} for i in range(8) if 0 <=nx<xr and 0 <=ny<yr ]
auto adjacent_eight_cells(int x, int y,         int xr,         int yr) { return AdjacentEightCellsBounded { x, y, 0 , xr, 0 , yr }; }

#include <algorithm>
#include <queue>

namespace suisen {
template<typename Cost>
class dijkstra {
    public:
        template <typename Transition>
        dijkstra(unsigned int n, Transition transition, unsigned int src) : _src(src) {
            _par.resize(n);
            _dist.assign(n, UNREACHABLE);
            _dist[src] = 0;
            using state = std::pair<Cost, unsigned int>;
            std::priority_queue<state, std::vector<state>, std::greater<state>> pq;
            pq.emplace(0, src);
            auto g = [&](unsigned int u) {
                return [&, u](unsigned int v, Cost new_cost) {
                    if (new_cost < _dist[v]) pq.emplace(_dist[v] = new_cost, v), _par[v] = u;
                };
            };
            while (pq.size()) {
                auto [du, u] = pq.top(); pq.pop();
                if (du == _dist[u]) transition(u, du, g(u));
            }
        }
        dijkstra(const std::vector<std::vector<std::pair<int, Cost>>> &g, unsigned int src) :
            dijkstra(g.size(), [&](int u, Cost du, auto f) { for (auto [v, c] : g[u]) f(v, du + c); }, src) {}
        std::vector<unsigned int> path_to(unsigned int t) const {
            assert(is_reachale(t));
            std::vector<unsigned int> path = {t};
            while (t != _src) path.push_back(t = _par[t]);
            std::reverse(path.begin(), path.end());
            return path;
        }
        Cost operator[](unsigned int t) const { return _dist[t]; }
        bool is_reachale   (unsigned int t) const { return _dist[t] != UNREACHABLE; }
        bool is_unreachable(unsigned int t) const { return _dist[t] == UNREACHABLE; }
    private:
        const Cost UNREACHABLE = std::numeric_limits<Cost>::max();
        const unsigned int _src;
        std::vector<Cost> _dist;
        std::vector<unsigned int> _par;
};
} // namespace suisen

constexpr long long inf = numeric_limits<long long>::max() / 2;

int main() {
    int n, m, k, t;
    read(n, m, k, t);

    vector special(n, vector<pair<int, int>>(m, { 0, 0 }));
    LOOP(k) {
        int a, b, c, d;
        read(a, b, c, d);
        --a, --b, --c;
        special[a][b] = { c, d };
    }

    const int l = (n - 1) + (m - 1);

    if (l <= t) {
        print(0);
        return 0;
    }

    const int max_l = 80 * (l + 1);

    auto make_state = [&](int i, int j, int q) {
        return (i * m + j) * (max_l + 1) + q;
    };
    auto decomp_state = [&](int u) {
        int ij = u / (max_l + 1);
        int i = ij / m, j = ij % m;
        int q = u % (max_l + 1);
        return tuple{ i, j, q };
    };

    const int end_state = (n * m) * (max_l + 1);
    dijkstra<long long> dij(
        end_state + 1,
        [&](int u, long long du, auto trans) {
            if (u == end_state) return;

            auto [i, j, q] = decomp_state(u);

            if (special[i][j].first) {
                auto [c, d] = special[i][j];
                while (true) {
                    q -= c;
                    du += d;
                    if (q <= 0) {
                        trans(end_state, du);
                        break;
                    }
                    trans(make_state(i, j, q), du);
                }
            } else {
                for (auto [ni, nj] : adjacent_four_cells(i, j, n, m)) {
                    int nq = q + 2 * (ni < i or nj < j);
                    if (nq <= max_l) {
                        trans(make_state(ni, nj, nq), du);
                    }
                }
            }
        },
        l - t
    );
    print(dij.is_reachale(end_state) ? dij[end_state] : -1);
}