結果

問題 No.2069 み世界数式
ユーザー KowerKoint2010KowerKoint2010
提出日時 2022-09-10 08:09:40
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 19 ms / 2,000 ms
コード長 19,837 bytes
コンパイル時間 3,049 ms
コンパイル使用メモリ 229,336 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-11-26 09:50:58
合計ジャッジ時間 4,887 ms
ジャッジサーバーID
(参考情報)
judge2 / judge4
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,820 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 2 ms
6,816 KB
testcase_03 AC 2 ms
6,816 KB
testcase_04 AC 2 ms
6,816 KB
testcase_05 AC 2 ms
6,820 KB
testcase_06 AC 2 ms
6,816 KB
testcase_07 AC 2 ms
6,820 KB
testcase_08 AC 2 ms
6,820 KB
testcase_09 AC 2 ms
6,820 KB
testcase_10 AC 2 ms
6,820 KB
testcase_11 AC 3 ms
6,816 KB
testcase_12 AC 4 ms
6,820 KB
testcase_13 AC 4 ms
6,820 KB
testcase_14 AC 3 ms
6,820 KB
testcase_15 AC 4 ms
6,820 KB
testcase_16 AC 8 ms
6,816 KB
testcase_17 AC 4 ms
6,820 KB
testcase_18 AC 6 ms
6,816 KB
testcase_19 AC 7 ms
6,816 KB
testcase_20 AC 6 ms
6,816 KB
testcase_21 AC 4 ms
6,820 KB
testcase_22 AC 8 ms
6,820 KB
testcase_23 AC 6 ms
6,816 KB
testcase_24 AC 5 ms
6,820 KB
testcase_25 AC 5 ms
6,816 KB
testcase_26 AC 6 ms
6,816 KB
testcase_27 AC 2 ms
6,820 KB
testcase_28 AC 2 ms
6,820 KB
testcase_29 AC 2 ms
6,816 KB
testcase_30 AC 2 ms
6,816 KB
testcase_31 AC 2 ms
6,820 KB
testcase_32 AC 2 ms
6,816 KB
testcase_33 AC 2 ms
6,820 KB
testcase_34 AC 2 ms
6,816 KB
testcase_35 AC 2 ms
6,820 KB
testcase_36 AC 2 ms
6,816 KB
testcase_37 AC 19 ms
6,816 KB
testcase_38 AC 7 ms
6,816 KB
testcase_39 AC 4 ms
6,816 KB
testcase_40 AC 2 ms
6,820 KB
testcase_41 AC 3 ms
6,820 KB
testcase_42 AC 2 ms
6,820 KB
testcase_43 AC 2 ms
6,816 KB
testcase_44 AC 3 ms
6,820 KB
権限があれば一括ダウンロードができます

ソースコード

diff #

#line 2 "library/KowerKoint/base.hpp"

#ifdef DEBUG
#define _GLIBCXX_DEBUG
#endif

#include <bits/stdc++.h>
using namespace std;

#define REP(i, n) for(int i = 0; i < (int)(n); i++)
#define FOR(i, a, b) for(ll i = a; i < (ll)(b); i++)
#define ALL(a) (a).begin(),(a).end()
#define END(...) { print(__VA_ARGS__); return; }

using VI = vector<int>;
using VVI = vector<VI>;
using VVVI = vector<VVI>;
using ll = long long;
using VL = vector<ll>;
using VVL = vector<VL>;
using VVVL = vector<VVL>;
using ull = unsigned long long;
using VUL = vector<ull>;
using VVUL = vector<VUL>;
using VVVUL = vector<VVUL>;
using VD = vector<double>;
using VVD = vector<VD>;
using VVVD = vector<VVD>;
using VS = vector<string>;
using VVS = vector<VS>;
using VVVS = vector<VVS>;
using VC = vector<char>;
using VVC = vector<VC>;
using VVVC = vector<VVC>;
using P = pair<int, int>;
using VP = vector<P>;
using VVP = vector<VP>;
using VVVP = vector<VVP>;
using LP = pair<ll, ll>;
using VLP = vector<LP>;
using VVLP = vector<VLP>;
using VVVLP = vector<VVLP>;

template <typename T>
using PQ = priority_queue<T>;
template <typename T>
using GPQ = priority_queue<T, vector<T>, greater<T>>;

constexpr int INF = 1001001001;
constexpr ll LINF = 1001001001001001001ll;
constexpr int DX[] = {1, 0, -1, 0};
constexpr int DY[] = {0, 1, 0, -1};

template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
    os << p.first << " " << p.second;
    return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
    is >> p.first >> p.second;
    return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
    for(int i = 0; i < (int) v.size(); i++) {
        os << v[i] << (i + 1 != (int) v.size() ? " " : "");
    }
    return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
    for(T &in : v) is >> in;
    return is;
}

void print() { cout << '\n'; }
template<typename T>
void print(const T &t) { cout << t << '\n'; }
template<typename Head, typename... Tail>
void print(const Head &head, const Tail &... tail) {
    cout << head << ' ';
    print(tail...);
}

#ifdef DEBUG
void dbg() { cerr << '\n'; }
template<typename T>
void dbg(const T &t) { cerr << t << '\n'; }
template<typename Head, typename... Tail>
void dbg(const Head &head, const Tail &... tail) {
    cerr << head << ' ';
    dbg(tail...);
}
#else
template<typename... Args>
void dbg(const Args &... args) {}
#endif

template<typename T>
vector<vector<T>> split(typename vector<T>::const_iterator begin, typename vector<T>::const_iterator end, T val) {
    vector<vector<T>> res;
    vector<T> cur;
    for(auto it = begin; it != end; it++) {
        if(*it == val) {
            res.push_back(cur);
            cur.clear();
        } else cur.push_back(*it);
    }
    res.push_back(cur);
    return res;
}

vector<string> split(typename string::const_iterator begin, typename string::const_iterator end, char val) {
    vector<string> res;
    string cur = "";
    for(auto it = begin; it != end; it++) {
        if(*it == val) {
            res.push_back(cur);
            cur.clear();
        } else cur.push_back(*it);
    }
    res.push_back(cur);
    return res;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template <typename T>
pair<VI, vector<T>> compress(const vector<T> &a) {
    int n = a.size();
    vector<T> x;
    REP(i, n) x.push_back(a[i]);
    sort(ALL(x)); x.erase(unique(ALL(x)), x.end());
    VI res(n);
    REP(i, n) res[i] = lower_bound(ALL(x), a[i]) - x.begin();
    return make_pair(res, x);
}

template <typename It>
auto rle(It begin, It end) {
    vector<pair<typename It::value_type, int>> res;
    if(begin == end) return res;
    auto pre = *begin;
    int num = 1;
    for(auto it = begin + 1; it != end; it++) {
        if(pre != *it) {
            res.emplace_back(pre, num);
            pre = *it;
            num = 1;
        } else num++;
    }
    res.emplace_back(pre, num);
    return res;
}

template <typename It>
vector<pair<typename It::value_type, int>> rle_sort(It begin, It end) {
    vector<typename It::value_type> cloned(begin, end);
    sort(ALL(cloned));
    auto e = rle(ALL(cloned));
    sort(ALL(e), [](const auto& l, const auto& r) { return l.second < r.second; });
    return e;
}

template <typename T>
pair<vector<T>, vector<T>> factorial(int n) {
    vector<T> res(n+1), rev(n+1);
    res[0] = 1;
    REP(i, n) res[i+1] = res[i] * (i+1);
    rev[n] = 1 / res[n];
    for(int i = n; i > 0; i--) {
        rev[i-1] = rev[i] * i;
    }
    return make_pair(res, rev);
}
#line 3 "library/KowerKoint/operator.hpp"

template <typename T>
T add_op(T a, T b) { return a + b; }
template <typename T>
T sub_op(T a, T b) { return a - b; }
template <typename T>
T zero_e() { return T(0); }
template <typename T>
T div_op(T a, T b) { return a / b; }
template <typename T>
T mult_op(T a, T b) { return a * b; }
template <typename T>
T one_e() { return T(1); }
template <typename T>
T xor_op(T a, T b) { return a ^ b; }
template <typename T>
T and_op(T a, T b) { return a & b; }
template <typename T>
T or_op(T a, T b) { return a | b; }
ll mod3() { return 998244353LL; }
ll mod7() { return 1000000007LL; }
ll mod9() { return 1000000009LL; }
template <typename T>
T max_op(T a, T b) { return max(a, b); }
template <typename T>
T min_op(T a, T b) { return min(a, b); }

template <typename T>
T max_e() { return numeric_limits<T>::max(); }
template <typename T>
T min_e() { return numeric_limits<T>::min(); }
#line 2 "library/KowerKoint/integer/extgcd.hpp"

ll extgcd(ll a, ll b, ll& x, ll& y) {
    x = 1, y = 0;
    ll nx = 0, ny = 1;
    while(b) {
        ll q = a / b;
        tie(a, b) = LP(b, a % b);
        tie(x, nx) = LP(nx, x - nx*q);
        tie(y, ny) = LP(ny, y - ny*q);
    }
    return a;
}
#line 2 "library/KowerKoint/integer/pow-mod.hpp"

ll inv_mod(ll n, ll m) {
    ll x, y;
    assert(extgcd(n, m, x, y) == 1);
    x %= m;
    if(x < 0) x += m;
    return x;
}

ll pow_mod(ll a, ll n, ll m) {
    if(n == 0) return 1LL;
    if(n < 0) return inv_mod(pow_mod(a, -n, m), m);
    ll res = 1;
    while(n) {
        if(n & 1) {
            res *= a;
            res %= m;
        }
        n >>= 1;
        a *= a;
        a %= m;
    }
    return res;
}
#line 4 "library/KowerKoint/integer/modint.hpp"

template <ll (*mod)()>
struct Modint {
    ll val;
    
    Modint(): val(0) {}

    Modint(ll x): val(x) {
        val %= mod();
        if(val < 0) val += mod();
    }

    Modint& operator+=(const Modint& r) {
        val += r.val;
        if(val >= mod()) val -= mod();
        return *this;
    }
    friend Modint operator+(const Modint& l, const Modint& r) {
        return Modint(l) += r;
    }

    Modint& operator-=(const Modint& r) {
        val -= r.val;
        if(val < 0) val += mod();
        return *this;
    }
    friend Modint operator-(const Modint& l, const Modint& r) {
        return Modint(l) -= r;
    }

    Modint& operator*=(const Modint& r) {
        val *= r.val;
        val %= mod();
        return *this;
    }
    Modint operator*(const Modint& r) {
        return (Modint(*this) *= r);
    }
    friend Modint operator*(const Modint& l, const Modint& r) {
        return Modint(l) *= r;
    }

    Modint pow(ll n) const {
        return Modint(pow_mod(val, n, mod()));
    }

    Modint inv() const {
        return Modint(inv_mod(val, mod()));
    }

    Modint& operator/=(const Modint& r) {
        return (*this *= r.inv());
    }
    friend Modint operator/(const Modint& l, const Modint& r) {
        return Modint(l) /= r;
    }

    Modint& operator^=(const ll n) {
        val = pow_mod(val, n, mod());
        return *this;
    }
    Modint operator^(const ll n) {
        return this->pow(n);
    }

    Modint operator+() const { return *this; }
    Modint operator-() const { return Modint() - *this; }

    Modint& operator++() {
        val++;
        if(val == mod()) val = 0LL;
        return *this;
    }
    Modint& operator++(int) {
        Modint res(*this);
        ++*this;
        return res;
    }

    Modint& operator--() {
        if(val == 0LL) val = mod();
        val--;
        return *this;
    }
    Modint& operator--(int) {
        Modint res(*this);
        --*this;
        return res;
    }

    friend bool operator==(const Modint& l, const Modint& r) {
        return l.val == r.val;
    }
    friend bool operator!=(const Modint& l, const Modint& r) {
        return l.val != r.val;
    }

    static pair<vector<Modint>, vector<Modint>> factorial(int n) {
        vector<Modint> fact(n+1), rfact(n+1);
        fact[0] = 1;
        REP(i, n) fact[i+1] = fact[i] * (i+1);
        rfact[n] = 1 / fact[n];
        for(int i = n-1; i >= 0; i--) rfact[i] = rfact[i+1] * (i+1);
        return {fact, rfact};
    }

    friend istream& operator>>(istream& is, Modint& mi) {
        is >> mi.val;
        return is;
    }

    friend ostream& operator<<(ostream& os, const Modint& mi) {
        os << mi.val;
        return os;
    }
};

using MI3 = Modint<mod3>;
using V3 = vector<MI3>;
using VV3 = vector<V3>;
using VVV3 = vector<VV3>;
using MI7 = Modint<mod7>;
using V7 = vector<MI7>;
using VV7 = vector<V7>;
using VVV7 = vector<VV7>;
using MI9 = Modint<mod9>;
using V9 = vector<MI9>;
using VV9 = vector<V9>;
using VVV9 = vector<VV9>;
#line 3 "library/KowerKoint/counting/counting.hpp"

template <typename T>
struct Counting {
    vector<T> fact, ifact;

    Counting() {}
    Counting(ll n) {
        expand(n);
    }

    void expand(ll n) {
        ll sz = (ll)fact.size();
        if(sz > n) return;
        fact.resize(n+1);
        ifact.resize(n+1);
        fact[0] = 1;
        FOR(i, max(1LL, sz), n+1) fact[i] = fact[i-1] * i;
        ifact[n] = 1 / fact[n];
        for(ll i = n-1; i >= sz; i--) ifact[i] = ifact[i+1] * (i+1);
    }

    T p(ll n, ll r) {
        assert(n >= r);
        assert(r >= 0);
        expand(n);
        return fact[n] * ifact[n-r];
    }

    T c(ll n, ll r) {
        assert(n >= r);
        assert(r >= 0);
        expand(n);
        return fact[n] * ifact[r] * ifact[n-r];
    }

    T h(ll n, ll r) {
        assert(n >= 0);
        assert(r >= 0);
        return c(n+r-1, r);
    }

    T stirling(ll n, ll k) {
        assert(n >= k);
        assert(k >= 0);
        if(n == 0) return 1;
        T res = 0;
        int sign = k%2? -1 : 1;
        expand(k);
        REP(i, k+1) {
            res += sign * ifact[i] * ifact[k-i] * T(i).pow(n);
            sign *= -1;
        }
        return res;
    }

    vector<vector<T>> stirling_table(ll n, ll k) {
        assert(n >= 0 && k >= 0);
        vector<vector<T>> res(n+1, vector<T>(k+1));
        res[0][0] = 1;
        FOR(i, 1, n+1) FOR(j, 1, k+1) {
            res[i][j] = res[i-1][j-1] + j * res[i-1][j];
        }
        return res;
    }

    T bell(ll n, ll k) {
        assert(n >= 0 && k >= 0);
        expand(k);
        vector<T> tmp(k+1);
        int sign = 1;
        tmp[0] = 1;
        FOR(i, 1, k+1) {
            sign *= -1;
            tmp[i] = tmp[i-1] + sign * ifact[i];
        }
        T res = 0;
        REP(i, k+1) {
            res += T(i).pow(n) * ifact[i] * tmp[k-i];
        }
        return res;
    }

    vector<vector<T>> partition_table(ll n, ll k) {
        assert(n >= 0);
        vector<vector<T>> res(n+1, vector<T>(k+1));
        REP(i, k+1) res[0][i] = 1;
        FOR(i, 1, n+1) FOR(j, 1, k+1) {
            res[i][j] = res[i][j-1] + (i<j? 0 : res[i-j][j]);
        }
        return res;
    }
};
#line 2 "library/KowerKoint/bit/bitset.hpp"

struct Bitset {
    private:
    void correct() {
        for(int i = n - (bnum-1)*64; i < 64; i++) {
            v[bnum-1] &= ~(1 << i);
        }
    }
    public:
    vector<ull> v;
    int n, bnum;
    Bitset(int n_ = 0) : n(n_) {
        bnum = (n+63) / 64;
        v.resize(bnum);
    }
    int operator[](int i) {
        return (v[i/64] >> (i%64)) & 1;
    }
    int count() {
        int c = 0;
        for (int i = 0; i < v.size(); i++) {
            c += __builtin_popcountll(v[i]);
        }
        return c;
    }
    int count_range(int l, int r) {
        int c = 0;
        int l2 = (l+63) / 64;
        int r2 = r / 64;
        for(int i = l2; i < r2; i++) {
            c += __builtin_popcountll(v[i]);
        }
        if(l < l2 * 64) {
            for(int i = l % 64; i < 64; i++) c += (v[l2-1] >> i) & 1;
        }
        if(r2 * 64 < r) {
            for(int i = 0; i < r % 64; i++) c += (v[r2] >> i) & 1;
        }
        return c;
    }
    bool all() {
        return count() == n;
    }
    bool any() {
        return count() > 0;
    }
    bool none() {
        return count() == 0;
    }
    void set(int i) {
        v[i / 64] |= 1ull << (i % 64);
    }
    void reset(int i) {
        v[i / 64] &= ~(1ull << (i % 64));
    }
    void flip(int i) {
        v[i / 64] ^= 1ull << (i % 64);
    }
    void resize(int n_) {
        n = n_;
        v.resize((n+63) / 64);
        correct();
    }
    void all_set() {
        fill(v.begin(), v.end(),  ~0ULL);
        correct();
    }
    void all_reset() {
        fill(v.begin(), v.end(), 0);
    }
    void all_flip() {
        for (int i = 0; i < v.size(); i++) {
            v[i] = ~v[i];
        }
        correct();
    }
    Bitset& operator&=(const Bitset& b) {
        for(int i = 0; i < min(bnum, b.bnum); i++) {
            v[i] &= b.v[i];
        }
        return *this;
    }
    Bitset operator&(const Bitset& b) const {
        return Bitset(*this) &= b;
    }
    Bitset& operator|=(const Bitset& b) {
        for(int i = 0; i < min(bnum, b.bnum); i++) {
            v[i] |= b.v[i];
        }
        correct();
        return *this;
    }
    Bitset operator|(const Bitset& b) const {
        return Bitset(*this) |= b;
    }
    Bitset& operator^=(const Bitset& b) {
        for(int i = 0; i < min(bnum, b.bnum); i++) {
            v[i] ^= b.v[i];
        }
        correct();
        return *this;
    }
    Bitset operator^(const Bitset& b) const {
        return Bitset(*this) ^= b;
    }
    Bitset operator~() const {
        Bitset b(*this);
        b.all_flip();
        return b;
    }
    bool operator==(const Bitset& b) const {
        return v == b.v;
    }
    bool operator!=(const Bitset& b) const {
        return v != b.v;
    }
    Bitset& operator<<=(int sz) {
        for(int i = bnum-1; i >= 0; i--) {
            if(i-sz/64 >= 0) v[i] = v[i-sz/64] << (sz%64);
            if(i-sz/64-1 >= 0) v[i] |= v[i-sz/64-1] >> (64-sz%64);
        }
        correct();
        return *this;
    }
    Bitset operator<<(int sz) const {
        return Bitset(*this) <<= sz;
    }
    Bitset& operator>>=(int sz) {
        for(int i = 0; i < bnum; i++) {
            if(i+sz/64 < bnum) v[i] = v[i+sz/64] >> (sz%64);
            if(i+sz/64+1 < bnum) v[i] |= v[i+sz/64+1] << (64-sz%64);
        }
        return *this;
    }
    Bitset operator>>(int sz) const {
        return Bitset(*this) >>= sz;
    }
};
#line 3 "Contests/main.cpp"

/* #include <atcoder/all> */
/* using namespace atcoder; */
/* #include "KowerKoint/expansion/ac-library/all.hpp" */

struct Component {
    int op_pos;
    Bitset cand;
};

int m, ans;
string expr;
map<P, Component> number, factor, term, expression;

void pre_number(int l, int r) {
    Bitset b(m+1);
    int res = 0;
    FOR(i, l, r) {
        res *= 10;
        res += expr[i] - '0';
    }
    b.set(res);
    number[P(l, r)] = {r, b};
}

void pre_expression(int, int);

void pre_factor(int l, int r) {
    if(expr[l] == '(') {
        pre_expression(l+1, r-1);
        factor[P(l, r)] = {l, expression[P(l+1,r-1)].cand};
    } else {
        pre_number(l, r);
        factor[P(l, r)] = number[P(l, r)];
    }
}

void pre_term(int l, int r) {
    int p = r-1;
    int blace = 0;
    while(p >= l && expr[p] != '&' || blace != 0) {
        if(expr[p] == ')') blace++;
        if(expr[p] == '(') blace--;
        p--;
    }
    if(p == l-1) {
        pre_factor(l, r);
        term[P(l, r)] = {p, factor[P(l, r)].cand};
    } else {
        Bitset b(m+1);
        pre_term(l, p);
        pre_factor(p+1, r);
        auto& bi = term[P(l, p)].cand;
        auto& bj = factor[P(p+1, r)].cand;
        REP(i, m+1) {
            if(!bi[i]) continue;
            REP(j, m+1) {
                if(!bj[j]) continue;
                if(i*j <= m) b.set(i*j);
                if(j!=0) b.set(i/j);
            }
        }
        term[P(l, r)] = {p, b};
    }
}

void pre_expression(int l, int r) {
    int p = r-1;
    int blace = 0;
    while(p >= l && expr[p] != '$' || blace != 0) {
        if(expr[p] == ')') blace++;
        if(expr[p] == '(') blace--;
        p--;
    }
    if(p == l-1) {
        pre_term(l, r);
        expression[P(l, r)] = {p, term[P(l, r)].cand};
    } else {
        Bitset b(m+1);
        pre_expression(l, p);
        pre_term(p+1, r);
        auto& bi = expression[P(l, p)].cand;
        auto& bj = term[P(p+1, r)].cand;
        REP(i, m+1) {
            if(!bi[i]) continue;
            REP(j, m+1) {
                if(!bj[j]) continue;
                if(i+j <= m) b.set(i+j);
                if(i-j>=0) b.set(i-j);
            }
        }
        expression[P(l, r)] = {p, b};
    }
}

void post_expression(int, int, int);

void post_factor(int l, int r, int target) {
    if(factor[P(l, r)].op_pos == l) post_expression(l+1, r-1, target);
}

void post_term(int l, int r, int target) {
    int p = term[P(l, r)].op_pos;
    if(p == l-1) post_factor(l, r, target);
    else {
        auto& bi = term[P(l, p)].cand;
        auto& bj = factor[P(p+1, r)].cand;
        REP(i, m+1) {
            if(!bi[i]) continue;
            REP(j, m+1) {
                if(!bj[j]) continue;
                if(i*j == target) {
                    expr[p] = '*';
                    post_term(l, p, i);
                    post_factor(p+1, r, j);
                    return;
                }
                if(j!=0&&i/j==target) {
                    expr[p] = '/';
                    post_term(l, p, i);
                    post_factor(p+1, r, j);
                    return;
                }
            }
        }
    }
}

void post_expression(int l, int r, int target) {
    int p = expression[P(l, r)].op_pos;
    if(p == l-1) post_term(l, r, target);
    else {
        auto& bi = expression[P(l, p)].cand;
        auto& bj = term[P(p+1, r)].cand;
        REP(i, m+1) {
            if(!bi[i]) continue;
            REP(j, m+1) {
                if(!bj[j]) continue;
                if(i+j == target) {
                    expr[p] = '+';
                    post_expression(l, p, i);
                    post_term(p+1, r, j);
                    return;
                }
                if(i-j == target) {
                    expr[p] = '-';
                    post_expression(l, p, i);
                    post_term(p+1, r, j);
                    return;
                }
            }
        }
    }
}

void solve(){
    cin >> m >> ans >> expr;
    pre_expression(0, expr.size());
    if(!expression[P(0, expr.size())].cand[ans]) print(-1);
    else {
        post_expression(0, expr.size(), ans);
        print(expr);
    }
}

// generated by oj-template v4.7.2 (https://github.com/online-judge-tools/template-generator)
int main() {
    // Fasterize input/output script
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(100);
    // scanf/printf user should delete this fasterize input/output script

    int t = 1;
    //cin >> t; // comment out if solving multi testcase
    for(int testCase = 1;testCase <= t;++testCase){
        solve();
    }
    return 0;
}
0