#706679 (C++17) No.1699 Unfair RPS

• 問題: No.1699 Unfair RPS
• ユーザー: tonakai
• 提出日時: 2021-10-10 16:33:55
• 言語: C++17 (gcc 13.3.0 + boost 1.89.0)
• 結果: WA
• 実行時間: -
• コード長: 62,236 bytes
• コンパイル時間: 6,386 ms
• コンパイル使用メモリ: 285,956 KB
• 最終ジャッジ日時: 2025-01-25 00:01:10
• ジャッジサーバーID （参考情報）: judge1 / judge1

ファイルパターン	結果
sample	WA * 2
other	WA * 9

ソースコード

#include<bits/stdc++.h>
using namespace std;
typedef unsigned int ui;
typedef unsigned long ul;
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> pll;
typedef pair<ld,ll> pdl;
typedef pair<ll,ld> pld;
typedef pair<ld,ld> pdd;
#ifdef _MSC_VER
#endif
namespace atcoder{namespace internal{int ceil_pow2(int n){int x=0;while((1U<<x)<(ui)(n))x++;return x;}constexpr int bsf_constexpr(ui n){int x=0;while(!(n&(1<<x)))x++;return x;}int bsf(ui n){
#ifdef _MSC_VER
ul index;_BitScanForward(&index,n);return index;
#else
return __builtin_ctz(n);
#endif
}}}
#ifdef _MSC_VER
#endif
#ifdef _MSC_VER
#endif
namespace atcoder{namespace internal{constexpr ll safe_mod(ll x,ll m){x%=m;if(x<0)x+=m;return x;}struct barrett{ui _m;ull im;explicit barrett(ui m):_m(m),im((ull)(-1)/m+1){}ui umod()const{return _m;}ui mul(ui a,ui b)const{ull z=a;z*=b;
#ifdef _MSC_VER
ull x;_umul128(z,im,&x);
#else
ull x=(ull)(((unsigned __int128)(z)*im)>>64);
#endif
ui v=(ui)(z-x*_m);if(_m<=v)v+=_m;return v;}};constexpr ll pow_mod_constexpr(ll x,ll n,int m){if(m==1)return 0;ui _m=(ui)(m);ull r=1,y=safe_mod(x,m);while(n){if(n&1)r=(r*y)%_m;y=(y*y)%_m;n>>=1;}return r;}
constexpr bool is_prime_constexpr(int n){if(n<=1)return false;if(n==2||n==7||n==61)return true;if(n%2==0)return false;ll d=n-1;while(d%2==0)d/=2;constexpr ll bases[3]={2,7,61};for(ll a:bases){ll t=d,y=pow_mod_constexpr(a,t,n);while(t!=n-1&&y!=1&&y!=n-1){y=y*y%n;t<<=1;}if(y!=n-1&&t%2==0)return false;}return true;}
template<int n>constexpr bool is_prime=is_prime_constexpr(n);constexpr pll inv_gcd(ll a,ll b){a=safe_mod(a, b);if(a==0)return{b,0};ll s=b,t=a,m0=0,m1=1;while(t){ll u=s/t;s-=t*u;m0-=m1*u;auto tmp=s;s=t;t=tmp;tmp=m0;m0=m1;m1=tmp;}if(m0<0)m0+=b/s;return{s,m0};}
constexpr int primitive_root_constexpr(int m){if(m==2)return 1;if(m==167772161)return 3;if(m==469762049)return 3;if(m==754974721)return 11;if(m==998244353)return 3;int divs[20]={};divs[0]=2;int cnt=1,x=(m-1)/2;while(x%2==0){x/=2;}for(int i=3;(ll)(i)*i<=x;i+=2){if(x%i==0){divs[cnt++]=i;while(x%i==0){x/=i;}}}if(x>1){divs[cnt++]=x;}for(int g=2;;g++){bool ok=true;for(int i=0;i<cnt;i++){if(pow_mod_constexpr(g,(m-1)/divs[i],m)==1){ok=false;break;}}if(ok)return g;}}
template<int m>constexpr int primitive_root=primitive_root_constexpr(m);ull floor_sum_unsigned(ull n,ull m,ull a,ull b){ull ans=0;while(1){if(a>=m){ans+=n*(n-1)/2*(a/m);a%=m;}if(b>=m){ans+=n*(b/m);b%=m;}ull y_max=a*n+b;if(y_max<m)break;n=(ull)(y_max/m);b=(ull)(y_max%m);swap(m,a);}return ans;}}}
namespace atcoder{namespace internal{
#ifndef _MSC_VER
template<class T>using is_signed_int128=typename conditional<is_same<T,__int128_t>::value||is_same<T, __int128>::value,true_type,false_type>::type;
template<class T>using is_unsigned_int128=typename conditional<is_same<T,__uint128_t>::value||is_same<T,unsigned __int128>::value,true_type,false_type>::type;
template<class T>using make_unsigned_int128=typename std::conditional<is_same<T,__int128_t>::value,__uint128_t,unsigned __int128>;
template<class T>using is_integral=typename conditional<is_integral<T>::value||is_signed_int128<T>::value||is_unsigned_int128<T>::value,true_type,false_type>::type;
template<class T>using is_signed_int=typename conditional<(is_integral<T>::value&&is_signed<T>::value)||is_signed_int128<T>::value,true_type,false_type>::type;
template <class T>using is_unsigned_int=typename conditional<(is_integral<T>::value&&is_unsigned<T>::value)||is_unsigned_int128<T>::value,true_type,false_type>::type;
template<class T>using to_unsigned=typename conditional<is_signed_int128<T>::value,make_unsigned_int128<T>,typename conditional<is_signed<T>::value,make_unsigned<T>,common_type<T>>::type>::type;
#else
template<class T>using is_integral=typename is_integral<T>;
template<class T>using is_signed_int=typename conditional<is_integral<T>::value&&is_signed<T>::value,true_type,false_type>::type;
template<class T>using is_unsigned_int=typename conditional<is_integral<T>::value&&is_unsigned<T>::value,true_type,false_type>::type;
template<class T>
using to_unsigned=typename conditional<is_signed_int<T>::value,make_unsigned<T>,common_type<T>>::type;
#endif
template<class T>using is_signed_int_t=enable_if_t<is_signed_int<T>::value>;
template<class T>using is_unsigned_int_t=enable_if_t<is_unsigned_int<T>::value>;
template<class T>using to_unsigned_t=typename to_unsigned<T>::type;}}
namespace atcoder{namespace internal{struct modint_base {};struct static_modint_base:modint_base{};
template<class T>using is_modint=is_base_of<modint_base,T>;
template<class T>using is_modint_t=enable_if_t<is_modint<T>::value>;}
template<int m,std::enable_if_t<(1<=m)>* =nullptr>struct static_modint:internal::static_modint_base{using mint=static_modint;public:static constexpr int mod(){return m;}static mint raw(int v){mint x;x._v=v;return x;}static_modint():_v(0){}
template<class T,internal::is_signed_int_t<T>* =nullptr>static_modint(T v){ll x=(ll)(v%(ll)(umod()));if(x<0)x+=umod();_v=(ui)(x);}
template<class T,internal::is_unsigned_int_t<T>* =nullptr>static_modint(T v){_v=(ui)(v%umod());}ui val()const{return _v;}
mint&operator++(){_v++;if(_v==umod())_v=0;return*this;}mint&operator--(){if(_v==0)_v=umod();_v--;return*this;}mint operator++(int){mint result=*this;++*this;return result;}mint operator--(int){mint result=*this;--*this;return result;}
mint&operator+=(const mint& rhs){_v+=rhs._v;if(_v>=umod())_v-=umod();return*this;}mint&operator-=(const mint& rhs){_v-=rhs._v;if(_v>=umod())_v+=umod();return*this;}mint&operator*=(const mint& rhs){ull z=_v;z*=rhs._v;_v=(ui)(z%umod());return*this;}mint&operator/=(const mint& rhs){return*this=*this*rhs.inv();}
mint operator+()const{return*this;}mint operator-()const{return mint()-*this;}
mint pow(ll n)const{assert(0<=n);mint x=*this,r=1;while(n){if(n&1)r*=x;x*=x;n>>=1;}return r;}
mint inv()const{if(prime){assert(_v);return pow(umod()-2);}else{auto eg=internal::inv_gcd(_v,m);assert(eg.first==1);return eg.second;}}
friend mint operator+(const mint&lhs,const mint&rhs){return mint(lhs)+=rhs;}friend mint operator-(const mint&lhs,const mint&rhs){return mint(lhs)-=rhs;}friend mint operator*(const mint&lhs,const mint&rhs){return mint(lhs)*=rhs;}friend mint operator/(const mint&lhs,const mint&rhs){return mint(lhs)/=rhs;}
friend bool operator==(const mint&lhs,const mint&rhs){return lhs._v==rhs._v;}friend bool operator!=(const mint&lhs,const mint&rhs){return lhs._v!=rhs._v;}
private:ui _v;static constexpr ui umod(){return m;}static constexpr bool prime=internal::is_prime<m>;};
template<int id>struct dynamic_modint:internal::modint_base{using mint=dynamic_modint;public:static int mod(){return(int)(bt.umod());}static void set_mod(int m){assert(1<=m);bt=internal::barrett(m);}static mint raw(int v){mint x;x._v=v;return x;}dynamic_modint():_v(0){}
template<class T,internal::is_signed_int_t<T>* =nullptr>dynamic_modint(T v){ll x=(ll)(v%(ll)(mod()));if(x<0)x+=mod();_v=(ui)(x);}
template<class T,internal::is_unsigned_int_t<T>* =nullptr>dynamic_modint(T v){_v=(ui)(v%mod());}ui val()const{return _v;}
mint&operator++(){_v++;if(_v==umod())_v=0;return*this;}mint&operator--(){if(_v==0)_v=umod();_v--;return*this;}mint operator++(int){mint result=*this;++*this;return result;}mint operator--(int){mint result=*this;--*this;return result;}
mint&operator+=(const mint&rhs){_v+=rhs._v;if(_v>=umod())_v-=umod();return*this;}mint&operator-=(const mint&rhs){_v+=mod()-rhs._v;if(_v>=umod())_v-=umod();return*this;}mint&operator*=(const mint&rhs){_v=bt.mul(_v,rhs._v);return*this;}mint&operator/=(const mint& rhs){return*this=*this*rhs.inv();}
mint operator+()const{return*this;}mint operator-()const{return mint()-*this;}
mint pow(ll n)const{assert(0<=n);mint x=*this,r=1;while(n){if(n&1)r*=x;x*=x;n>>=1;}return r;}
mint inv()const{auto eg=internal::inv_gcd(_v,mod());assert(eg.first==1);return eg.second;}
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
 
  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
 
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
 
namespace internal {
 
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
 
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
 
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
 
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
 
}  // namespace internal
 
}  // namespace atcoder
 
 
namespace atcoder {
 
namespace internal {
 
template <class mint,
          int g = internal::primitive_root<mint::mod()>,
          internal::is_static_modint_t<mint>* = nullptr>
struct fft_info {
    static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);
    std::array<mint, rank2 + 1> root;   // root[i]^(2^i) == 1
    std::array<mint, rank2 + 1> iroot;  // root[i] * iroot[i] == 1
 
    std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
    std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;
 
    std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
    std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;
 
    fft_info() {
        root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
        iroot[rank2] = root[rank2].inv();
        for (int i = rank2 - 1; i >= 0; i--) {
            root[i] = root[i + 1] * root[i + 1];
            iroot[i] = iroot[i + 1] * iroot[i + 1];
        }
 
        {
            mint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 2; i++) {
                rate2[i] = root[i + 2] * prod;
                irate2[i] = iroot[i + 2] * iprod;
                prod *= iroot[i + 2];
                iprod *= root[i + 2];
            }
        }
        {
            mint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 3; i++) {
                rate3[i] = root[i + 3] * prod;
                irate3[i] = iroot[i + 3] * iprod;
                prod *= iroot[i + 3];
                iprod *= root[i + 3];
            }
        }
    }
};
 
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
    int n = int(a.size());
    int h = internal::ceil_pow2(n);
 
    static const fft_info<mint> info;
 
    int len = 0;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while (len < h) {
        if (h - len == 1) {
            int p = 1 << (h - len - 1);
            mint rot = 1;
            for (int s = 0; s < (1 << len); s++) {
                int offset = s << (h - len);
                for (int i = 0; i < p; i++) {
                    auto l = a[i + offset];
                    auto r = a[i + offset + p] * rot;
                    a[i + offset] = l + r;
                    a[i + offset + p] = l - r;
                }
                if (s + 1 != (1 << len))
                    rot *= info.rate2[bsf(~(unsigned int)(s))];
            }
            len++;
        } else {
            int p = 1 << (h - len - 2);
            mint rot = 1, imag = info.root[2];
            for (int s = 0; s < (1 << len); s++) {
                mint rot2 = rot * rot;
                mint rot3 = rot2 * rot;
                int offset = s << (h - len);
                for (int i = 0; i < p; i++) {
                    auto mod2 = 1ULL * mint::mod() * mint::mod();
                    auto a0 = 1ULL * a[i + offset].val();
                    auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
                    auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
                    auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
                    auto a1na3imag =
                        1ULL * mint(a1 + mod2 - a3).val() * imag.val();
                    auto na2 = mod2 - a2;
                    a[i + offset] = a0 + a2 + a1 + a3;
                    a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
                    a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
                    a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
                }
                if (s + 1 != (1 << len))
                    rot *= info.rate3[bsf(~(unsigned int)(s))];
            }
            len += 2;
        }
    }
}
 
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
    int n = int(a.size());
    int h = internal::ceil_pow2(n);
 
    static const fft_info<mint> info;
 
    int len = h;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while (len) {
        if (len == 1) {
            int p = 1 << (h - len);
            mint irot = 1;
            for (int s = 0; s < (1 << (len - 1)); s++) {
                int offset = s << (h - len + 1);
                for (int i = 0; i < p; i++) {
                    auto l = a[i + offset];
                    auto r = a[i + offset + p];
                    a[i + offset] = l + r;
                    a[i + offset + p] =
                        (unsigned long long)(mint::mod() + l.val() - r.val()) *
                        irot.val();
                    ;
                }
                if (s + 1 != (1 << (len - 1)))
                    irot *= info.irate2[bsf(~(unsigned int)(s))];
            }
            len--;
        } else {
            int p = 1 << (h - len);
            mint irot = 1, iimag = info.iroot[2];
            for (int s = 0; s < (1 << (len - 2)); s++) {
                mint irot2 = irot * irot;
                mint irot3 = irot2 * irot;
                int offset = s << (h - len + 2);
                for (int i = 0; i < p; i++) {
                    auto a0 = 1ULL * a[i + offset + 0 * p].val();
                    auto a1 = 1ULL * a[i + offset + 1 * p].val();
                    auto a2 = 1ULL * a[i + offset + 2 * p].val();
                    auto a3 = 1ULL * a[i + offset + 3 * p].val();
 
                    auto a2na3iimag =
                        1ULL *
                        mint((mint::mod() + a2 - a3) * iimag.val()).val();
 
                    a[i + offset] = a0 + a1 + a2 + a3;
                    a[i + offset + 1 * p] =
                        (a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
                    a[i + offset + 2 * p] =
                        (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
                        irot2.val();
                    a[i + offset + 3 * p] =
                        (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
                        irot3.val();
                }
                if (s + 1 != (1 << (len - 2)))
                    irot *= info.irate3[bsf(~(unsigned int)(s))];
            }
            len -= 2;
        }
    }
}
 
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint>& a,
                                    const std::vector<mint>& b) {
    int n = int(a.size()), m = int(b.size());
    std::vector<mint> ans(n + m - 1);
    if (n < m) {
        for (int j = 0; j < m; j++) {
            for (int i = 0; i < n; i++) {
                ans[i + j] += a[i] * b[j];
            }
        }
    } else {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                ans[i + j] += a[i] * b[j];
            }
        }
    }
    return ans;
}
 
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
    int n = int(a.size()), m = int(b.size());
    int z = 1 << internal::ceil_pow2(n + m - 1);
    a.resize(z);
    internal::butterfly(a);
    b.resize(z);
    internal::butterfly(b);
    for (int i = 0; i < z; i++) {
        a[i] *= b[i];
    }
    internal::butterfly_inv(a);
    a.resize(n + m - 1);
    mint iz = mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
    return a;
}
 
}  // namespace internal
 
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
}
 
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(const std::vector<mint>& a,
                              const std::vector<mint>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
}
 
template <unsigned int mod = 998244353,
          class T,
          std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
 
    using mint = static_modint<mod>;
    std::vector<mint> a2(n), b2(m);
    for (int i = 0; i < n; i++) {
        a2[i] = mint(a[i]);
    }
    for (int i = 0; i < m; i++) {
        b2[i] = mint(b[i]);
    }
    auto c2 = convolution(move(a2), move(b2));
    std::vector<T> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        c[i] = c2[i].val();
    }
    return c;
}
 
std::vector<long long> convolution_ll(const std::vector<long long>& a,
                                      const std::vector<long long>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
 
    static constexpr unsigned long long MOD1 = 754974721;  // 2^24
    static constexpr unsigned long long MOD2 = 167772161;  // 2^25
    static constexpr unsigned long long MOD3 = 469762049;  // 2^26
    static constexpr unsigned long long M2M3 = MOD2 * MOD3;
    static constexpr unsigned long long M1M3 = MOD1 * MOD3;
    static constexpr unsigned long long M1M2 = MOD1 * MOD2;
    static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
 
    static constexpr unsigned long long i1 =
        internal::inv_gcd(MOD2 * MOD3, MOD1).second;
    static constexpr unsigned long long i2 =
        internal::inv_gcd(MOD1 * MOD3, MOD2).second;
    static constexpr unsigned long long i3 =
        internal::inv_gcd(MOD1 * MOD2, MOD3).second;
 
    auto c1 = convolution<MOD1>(a, b);
    auto c2 = convolution<MOD2>(a, b);
    auto c3 = convolution<MOD3>(a, b);
 
    std::vector<long long> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        unsigned long long x = 0;
        x += (c1[i] * i1) % MOD1 * M2M3;
        x += (c2[i] * i2) % MOD2 * M1M3;
        x += (c3[i] * i3) % MOD3 * M1M2;
        long long diff =
            c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
        if (diff < 0) diff += MOD1;
        static constexpr unsigned long long offset[5] = {
            0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
        x -= offset[diff % 5];
        c[i] = x;
    }
 
    return c;
}
 
}  // namespace atcoder
namespace atcoder {
 
struct dsu {
  public:
    dsu() : _n(0) {}
    explicit dsu(int n) : _n(n), parent_or_size(n, -1) {}
 
    int merge(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) return x;
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        return x;
    }
 
    bool same(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }
 
    int leader(int a) {
        assert(0 <= a && a < _n);
        if (parent_or_size[a] < 0) return a;
        return parent_or_size[a] = leader(parent_or_size[a]);
    }
 
    int size(int a) {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }
 
    std::vector<std::vector<int>> groups() {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
            std::remove_if(result.begin(), result.end(),
                           [&](const std::vector<int>& v) { return v.empty(); }),
            result.end());
        return result;
    }
 
  private:
    int _n;
    std::vector<int> parent_or_size;
};
 
}  // namespace atcoder
 
 
#include <cassert>
#include <vector>
 
 
namespace atcoder {
 
template <class T> struct fenwick_tree {
    using U = internal::to_unsigned_t<T>;
 
  public:
    fenwick_tree() : _n(0) {}
    explicit fenwick_tree(int n) : _n(n), data(n) {}
 
    void add(int p, T x) {
        assert(0 <= p && p < _n);
        p++;
        while (p <= _n) {
            data[p - 1] += U(x);
            p += p & -p;
        }
    }
 
    T sum(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        return sum(r) - sum(l);
    }
 
  private:
    int _n;
    std::vector<U> data;
 
    U sum(int r) {
        U s = 0;
        while (r > 0) {
            s += data[r - 1];
            r -= r & -r;
        }
        return s;
    }
};
 
}  // namespace atcoder
namespace atcoder {
 
template <class S,
          S (*op)(S, S),
          S (*e)(),
          class F,
          S (*mapping)(F, S),
          F (*composition)(F, F),
          F (*id)()>
struct lazy_segtree {
  public:
    lazy_segtree() : lazy_segtree(0) {}
    explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
    explicit lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        lz = std::vector<F>(size, id());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }
 
    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }
 
    S get(int p) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }
 
    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return e();
 
        l += size;
        r += size;
 
        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }
 
        S sml = e(), smr = e();
        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
 
        return op(sml, smr);
    }
 
    S all_prod() { return d[1]; }
 
    void apply(int p, F f) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = mapping(f, d[p]);
        for (int i = 1; i <= log; i++) update(p >> i);
    }
    void apply(int l, int r, F f) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return;
 
        l += size;
        r += size;
 
        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }
 
        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }
 
        for (int i = 1; i <= log; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }
 
    template <bool (*g)(S)> int max_right(int l) {
        return max_right(l, [](S x) { return g(x); });
    }
    template <class G> int max_right(int l, G g) {
        assert(0 <= l && l <= _n);
        assert(g(e()));
        if (l == _n) return _n;
        l += size;
        for (int i = log; i >= 1; i--) push(l >> i);
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!g(op(sm, d[l]))) {
                while (l < size) {
                    push(l);
                    l = (2 * l);
                    if (g(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }
 
    template <bool (*g)(S)> int min_left(int r) {
        return min_left(r, [](S x) { return g(x); });
    }
    template <class G> int min_left(int r, G g) {
        assert(0 <= r && r <= _n);
        assert(g(e()));
        if (r == 0) return 0;
        r += size;
        for (int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!g(op(d[r], sm))) {
                while (r < size) {
                    push(r);
                    r = (2 * r + 1);
                    if (g(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }
 
  private:
    int _n, size, log;
    std::vector<S> d;
    std::vector<F> lz;
 
    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
    void all_apply(int k, F f) {
        d[k] = mapping(f, d[k]);
        if (k < size) lz[k] = composition(f, lz[k]);
    }
    void push(int k) {
        all_apply(2 * k, lz[k]);
        all_apply(2 * k + 1, lz[k]);
        lz[k] = id();
    }
};
 
}  // namespace atcoder
namespace atcoder {
 
long long pow_mod(long long x, long long n, int m) {
    assert(0 <= n && 1 <= m);
    if (m == 1) return 0;
    internal::barrett bt((unsigned int)(m));
    unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
    while (n) {
        if (n & 1) r = bt.mul(r, y);
        y = bt.mul(y, y);
        n >>= 1;
    }
    return r;
}
 
long long inv_mod(long long x, long long m) {
    assert(1 <= m);
    auto z = internal::inv_gcd(x, m);
    assert(z.first == 1);
    return z.second;
}
 
std::pair<long long, long long> crt(const std::vector<long long>& r,
                                    const std::vector<long long>& m) {
    assert(r.size() == m.size());
    int n = int(r.size());
    long long r0 = 0, m0 = 1;
    for (int i = 0; i < n; i++) {
        assert(1 <= m[i]);
        long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
        if (m0 < m1) {
            std::swap(r0, r1);
            std::swap(m0, m1);
        }
        if (m0 % m1 == 0) {
            if (r0 % m1 != r1) return {0, 0};
            continue;
        }
 
 
        long long g, im;
        std::tie(g, im) = internal::inv_gcd(m0, m1);
 
        long long u1 = (m1 / g);
        if ((r1 - r0) % g) return {0, 0};
 
        long long x = (r1 - r0) / g % u1 * im % u1;
 
        r0 += x * m0;
        m0 *= u1;  // -> lcm(m0, m1)
        if (r0 < 0) r0 += m0;
    }
    return {r0, m0};
}
 
long long floor_sum(long long n, long long m, long long a, long long b) {
    assert(0 <= n && n < (1LL << 32));
    assert(1 <= m && m < (1LL << 32));
    unsigned long long ans = 0;
    if (a < 0) {
        unsigned long long a2 = internal::safe_mod(a, m);
        ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m);
        a = a2;
    }
    if (b < 0) {
        unsigned long long b2 = internal::safe_mod(b, m);
        ans -= 1ULL * n * ((b2 - b) / m);
        b = b2;
    }
    return ans + internal::floor_sum_unsigned(n, m, a, b);
}
 
}  // namespace atcoder
namespace atcoder {
 
namespace internal {
 
template <class T> struct simple_queue {
    std::vector<T> payload;
    int pos = 0;
    void reserve(int n) { payload.reserve(n); }
    int size() const { return int(payload.size()) - pos; }
    bool empty() const { return pos == int(payload.size()); }
    void push(const T& t) { payload.push_back(t); }
    T& front() { return payload[pos]; }
    void clear() {
        payload.clear();
        pos = 0;
    }
    void pop() { pos++; }
};
 
}  // namespace internal
 
}  // namespace atcoder
 
 
namespace atcoder {
 
template <class Cap> struct mf_graph {
  public:
    mf_graph() : _n(0) {}
    explicit mf_graph(int n) : _n(n), g(n) {}
 
    int add_edge(int from, int to, Cap cap) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        assert(0 <= cap);
        int m = int(pos.size());
        pos.push_back({from, int(g[from].size())});
        int from_id = int(g[from].size());
        int to_id = int(g[to].size());
        if (from == to) to_id++;
        g[from].push_back(_edge{to, to_id, cap});
        g[to].push_back(_edge{from, from_id, 0});
        return m;
    }
 
    struct edge {
        int from, to;
        Cap cap, flow;
    };
 
    edge get_edge(int i) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        auto _e = g[pos[i].first][pos[i].second];
        auto _re = g[_e.to][_e.rev];
        return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap};
    }
    std::vector<edge> edges() {
        int m = int(pos.size());
        std::vector<edge> result;
        for (int i = 0; i < m; i++) {
            result.push_back(get_edge(i));
        }
        return result;
    }
    void change_edge(int i, Cap new_cap, Cap new_flow) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        assert(0 <= new_flow && new_flow <= new_cap);
        auto& _e = g[pos[i].first][pos[i].second];
        auto& _re = g[_e.to][_e.rev];
        _e.cap = new_cap - new_flow;
        _re.cap = new_flow;
    }
 
    Cap flow(int s, int t) {
        return flow(s, t, std::numeric_limits<Cap>::max());
    }
    Cap flow(int s, int t, Cap flow_limit) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);
 
        std::vector<int> level(_n), iter(_n);
        internal::simple_queue<int> que;
 
        auto bfs = [&]() {
            std::fill(level.begin(), level.end(), -1);
            level[s] = 0;
            que.clear();
            que.push(s);
            while (!que.empty()) {
                int v = que.front();
                que.pop();
                for (auto e : g[v]) {
                    if (e.cap == 0 || level[e.to] >= 0) continue;
                    level[e.to] = level[v] + 1;
                    if (e.to == t) return;
                    que.push(e.to);
                }
            }
        };
        auto dfs = [&](auto self, int v, Cap up) {
            if (v == s) return up;
            Cap res = 0;
            int level_v = level[v];
            for (int& i = iter[v]; i < int(g[v].size()); i++) {
                _edge& e = g[v][i];
                if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;
                Cap d =
                    self(self, e.to, std::min(up - res, g[e.to][e.rev].cap));
                if (d <= 0) continue;
                g[v][i].cap += d;
                g[e.to][e.rev].cap -= d;
                res += d;
                if (res == up) return res;
            }
            level[v] = _n;
            return res;
        };
 
        Cap flow = 0;
        while (flow < flow_limit) {
            bfs();
            if (level[t] == -1) break;
            std::fill(iter.begin(), iter.end(), 0);
            Cap f = dfs(dfs, t, flow_limit - flow);
            if (!f) break;
            flow += f;
        }
        return flow;
    }
 
    std::vector<bool> min_cut(int s) {
        std::vector<bool> visited(_n);
        internal::simple_queue<int> que;
        que.push(s);
        while (!que.empty()) {
            int p = que.front();
            que.pop();
            visited[p] = true;
            for (auto e : g[p]) {
                if (e.cap && !visited[e.to]) {
                    visited[e.to] = true;
                    que.push(e.to);
                }
            }
        }
        return visited;
    }
 
  private:
    int _n;
    struct _edge {
        int to, rev;
        Cap cap;
    };
    std::vector<std::pair<int, int>> pos;
    std::vector<std::vector<_edge>> g;
};
 
}  // namespace atcoder
namespace atcoder {
namespace internal {
 
template <class E> struct csr {
    std::vector<int> start;
    std::vector<E> elist;
    explicit csr(int n, const std::vector<std::pair<int, E>>& edges)
        : start(n + 1), elist(edges.size()) {
        for (auto e : edges) {
            start[e.first + 1]++;
        }
        for (int i = 1; i <= n; i++) {
            start[i] += start[i - 1];
        }
        auto counter = start;
        for (auto e : edges) {
            elist[counter[e.first]++] = e.second;
        }
    }
};
 
}  // namespace internal
 
}  // namespace atcoder
 
 
namespace atcoder {
 
template <class Cap, class Cost> struct mcf_graph {
  public:
    mcf_graph() {}
    explicit mcf_graph(int n) : _n(n) {}
 
    int add_edge(int from, int to, Cap cap, Cost cost) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        assert(0 <= cap);
        assert(0 <= cost);
        int m = int(_edges.size());
        _edges.push_back({from, to, cap, 0, cost});
        return m;
    }
 
    struct edge {
        int from, to;
        Cap cap, flow;
        Cost cost;
    };
 
    edge get_edge(int i) {
        int m = int(_edges.size());
        assert(0 <= i && i < m);
        return _edges[i];
    }
    std::vector<edge> edges() { return _edges; }
 
    std::pair<Cap, Cost> flow(int s, int t) {
        return flow(s, t, std::numeric_limits<Cap>::max());
    }
    std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) {
        return slope(s, t, flow_limit).back();
    }
    std::vector<std::pair<Cap, Cost>> slope(int s, int t) {
        return slope(s, t, std::numeric_limits<Cap>::max());
    }
    std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);
 
        int m = int(_edges.size());
        std::vector<int> edge_idx(m);
 
        auto g = [&]() {
            std::vector<int> degree(_n), redge_idx(m);
            std::vector<std::pair<int, _edge>> elist;
            elist.reserve(2 * m);
            for (int i = 0; i < m; i++) {
                auto e = _edges[i];
                edge_idx[i] = degree[e.from]++;
                redge_idx[i] = degree[e.to]++;
                elist.push_back({e.from, {e.to, -1, e.cap - e.flow, e.cost}});
                elist.push_back({e.to, {e.from, -1, e.flow, -e.cost}});
            }
            auto _g = internal::csr<_edge>(_n, elist);
            for (int i = 0; i < m; i++) {
                auto e = _edges[i];
                edge_idx[i] += _g.start[e.from];
                redge_idx[i] += _g.start[e.to];
                _g.elist[edge_idx[i]].rev = redge_idx[i];
                _g.elist[redge_idx[i]].rev = edge_idx[i];
            }
            return _g;
        }();
 
        auto result = slope(g, s, t, flow_limit);
 
        for (int i = 0; i < m; i++) {
            auto e = g.elist[edge_idx[i]];
            _edges[i].flow = _edges[i].cap - e.cap;
        }
 
        return result;
    }
 
  private:
    int _n;
    std::vector<edge> _edges;
 
    struct _edge {
        int to, rev;
        Cap cap;
        Cost cost;
    };
 
    std::vector<std::pair<Cap, Cost>> slope(internal::csr<_edge>& g,
                                            int s,
                                            int t,
                                            Cap flow_limit) {
 
        std::vector<std::pair<Cost, Cost>> dual_dist(_n);
        std::vector<int> prev_e(_n);
        std::vector<bool> vis(_n);
        struct Q {
            Cost key;
            int to;
            bool operator<(Q r) const { return key > r.key; }
        };
        std::vector<int> que_min;
        std::vector<Q> que;
        auto dual_ref = [&]() {
            for (int i = 0; i < _n; i++) {
                dual_dist[i].second = std::numeric_limits<Cost>::max();
            }
            std::fill(vis.begin(), vis.end(), false);
            que_min.clear();
            que.clear();
 
            size_t heap_r = 0;
 
            dual_dist[s].second = 0;
            que_min.push_back(s);
            while (!que_min.empty() || !que.empty()) {
                int v;
                if (!que_min.empty()) {
                    v = que_min.back();
                    que_min.pop_back();
                } else {
                    while (heap_r < que.size()) {
                        heap_r++;
                        std::push_heap(que.begin(), que.begin() + heap_r);
                    }
                    v = que.front().to;
                    std::pop_heap(que.begin(), que.end());
                    que.pop_back();
                    heap_r--;
                }
                if (vis[v]) continue;
                vis[v] = true;
                if (v == t) break;
                Cost dual_v = dual_dist[v].first, dist_v = dual_dist[v].second;
                for (int i = g.start[v]; i < g.start[v + 1]; i++) {
                    auto e = g.elist[i];
                    if (!e.cap) continue;
                    Cost cost = e.cost - dual_dist[e.to].first + dual_v;
                    if (dual_dist[e.to].second - dist_v > cost) {
                        Cost dist_to = dist_v + cost;
                        dual_dist[e.to].second = dist_to;
                        prev_e[e.to] = e.rev;
                        if (dist_to == dist_v) {
                            que_min.push_back(e.to);
                        } else {
                            que.push_back(Q{dist_to, e.to});
                        }
                    }
                }
            }
            if (!vis[t]) {
                return false;
            }
 
            for (int v = 0; v < _n; v++) {
                if (!vis[v]) continue;
                dual_dist[v].first -= dual_dist[t].second - dual_dist[v].second;
            }
            return true;
        };
        Cap flow = 0;
        Cost cost = 0, prev_cost_per_flow = -1;
        std::vector<std::pair<Cap, Cost>> result = {{Cap(0), Cost(0)}};
        while (flow < flow_limit) {
            if (!dual_ref()) break;
            Cap c = flow_limit - flow;
            for (int v = t; v != s; v = g.elist[prev_e[v]].to) {
                c = std::min(c, g.elist[g.elist[prev_e[v]].rev].cap);
            }
            for (int v = t; v != s; v = g.elist[prev_e[v]].to) {
                auto& e = g.elist[prev_e[v]];
                e.cap += c;
                g.elist[e.rev].cap -= c;
            }
            Cost d = -dual_dist[s].first;
            flow += c;
            cost += c * d;
            if (prev_cost_per_flow == d) {
                result.pop_back();
            }
            result.push_back({flow, cost});
            prev_cost_per_flow = d;
        }
        return result;
    }
};
 
}  // namespace atcoder
namespace atcoder {
namespace internal {
 
struct scc_graph {
  public:
    explicit scc_graph(int n) : _n(n) {}
 
    int num_vertices() { return _n; }
 
    void add_edge(int from, int to) { edges.push_back({from, {to}}); }
 
    std::pair<int, std::vector<int>> scc_ids() {
        auto g = csr<edge>(_n, edges);
        int now_ord = 0, group_num = 0;
        std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);
        visited.reserve(_n);
        auto dfs = [&](auto self, int v) -> void {
            low[v] = ord[v] = now_ord++;
            visited.push_back(v);
            for (int i = g.start[v]; i < g.start[v + 1]; i++) {
                auto to = g.elist[i].to;
                if (ord[to] == -1) {
                    self(self, to);
                    low[v] = std::min(low[v], low[to]);
                } else {
                    low[v] = std::min(low[v], ord[to]);
                }
            }
            if (low[v] == ord[v]) {
                while (true) {
                    int u = visited.back();
                    visited.pop_back();
                    ord[u] = _n;
                    ids[u] = group_num;
                    if (u == v) break;
                }
                group_num++;
            }
        };
        for (int i = 0; i < _n; i++) {
            if (ord[i] == -1) dfs(dfs, i);
        }
        for (auto& x : ids) {
            x = group_num - 1 - x;
        }
        return {group_num, ids};
    }
 
    std::vector<std::vector<int>> scc() {
        auto ids = scc_ids();
        int group_num = ids.first;
        std::vector<int> counts(group_num);
        for (auto x : ids.second) counts[x]++;
        std::vector<std::vector<int>> groups(ids.first);
        for (int i = 0; i < group_num; i++) {
            groups[i].reserve(counts[i]);
        }
        for (int i = 0; i < _n; i++) {
            groups[ids.second[i]].push_back(i);
        }
        return groups;
    }
 
  private:
    int _n;
    struct edge {
        int to;
    };
    std::vector<std::pair<int, edge>> edges;
};
 
}  // namespace internal
 
}  // namespace atcoder
 
 
namespace atcoder {
 
struct scc_graph {
  public:
    scc_graph() : internal(0) {}
    explicit scc_graph(int n) : internal(n) {}
 
    void add_edge(int from, int to) {
        int n = internal.num_vertices();
        assert(0 <= from && from < n);
        assert(0 <= to && to < n);
        internal.add_edge(from, to);
    }
 
    std::vector<std::vector<int>> scc() { return internal.scc(); }
 
  private:
    internal::scc_graph internal;
};
 
}  // namespace atcoder
namespace atcoder {
 
template <class S, S (*op)(S, S), S (*e)()> struct segtree {
  public:
    segtree() : segtree(0) {}
    explicit segtree(int n) : segtree(std::vector<S>(n, e())) {}
    explicit segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }
 
    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }
 
    S get(int p) const {
        assert(0 <= p && p < _n);
        return d[p + size];
    }
 
    S prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        S sml = e(), smr = e();
        l += size;
        r += size;
 
        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }
 
    S all_prod() const { return d[1]; }
 
    template <bool (*f)(S)> int max_right(int l) const {
        return max_right(l, [](S x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) const {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }
 
    template <bool (*f)(S)> int min_left(int r) const {
        return min_left(r, [](S x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) const {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }
 
  private:
    int _n, size, log;
    std::vector<S> d;
 
    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};
 
}  // namespace atcoder
namespace atcoder {
 
namespace internal {
 
std::vector<int> sa_naive(const std::vector<int>& s) {
    int n = int(s.size());
    std::vector<int> sa(n);
    std::iota(sa.begin(), sa.end(), 0);
    std::sort(sa.begin(), sa.end(), [&](int l, int r) {
        if (l == r) return false;
        while (l < n && r < n) {
            if (s[l] != s[r]) return s[l] < s[r];
            l++;
            r++;
        }
        return l == n;
    });
    return sa;
}
 
std::vector<int> sa_doubling(const std::vector<int>& s) {
    int n = int(s.size());
    std::vector<int> sa(n), rnk = s, tmp(n);
    std::iota(sa.begin(), sa.end(), 0);
    for (int k = 1; k < n; k *= 2) {
        auto cmp = [&](int x, int y) {
            if (rnk[x] != rnk[y]) return rnk[x] < rnk[y];
            int rx = x + k < n ? rnk[x + k] : -1;
            int ry = y + k < n ? rnk[y + k] : -1;
            return rx < ry;
        };
        std::sort(sa.begin(), sa.end(), cmp);
        tmp[sa[0]] = 0;
        for (int i = 1; i < n; i++) {
            tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0);
        }
        std::swap(tmp, rnk);
    }
    return sa;
}
 
template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40>
std::vector<int> sa_is(const std::vector<int>& s, int upper) {
    int n = int(s.size());
    if (n == 0) return {};
    if (n == 1) return {0};
    if (n == 2) {
        if (s[0] < s[1]) {
            return {0, 1};
        } else {
            return {1, 0};
        }
    }
    if (n < THRESHOLD_NAIVE) {
        return sa_naive(s);
    }
    if (n < THRESHOLD_DOUBLING) {
        return sa_doubling(s);
    }
 
    std::vector<int> sa(n);
    std::vector<bool> ls(n);
    for (int i = n - 2; i >= 0; i--) {
        ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]);
    }
    std::vector<int> sum_l(upper + 1), sum_s(upper + 1);
    for (int i = 0; i < n; i++) {
        if (!ls[i]) {
            sum_s[s[i]]++;
        } else {
            sum_l[s[i] + 1]++;
        }
    }
    for (int i = 0; i <= upper; i++) {
        sum_s[i] += sum_l[i];
        if (i < upper) sum_l[i + 1] += sum_s[i];
    }
 
    auto induce = [&](const std::vector<int>& lms) {
        std::fill(sa.begin(), sa.end(), -1);
        std::vector<int> buf(upper + 1);
        std::copy(sum_s.begin(), sum_s.end(), buf.begin());
        for (auto d : lms) {
            if (d == n) continue;
            sa[buf[s[d]]++] = d;
        }
        std::copy(sum_l.begin(), sum_l.end(), buf.begin());
        sa[buf[s[n - 1]]++] = n - 1;
        for (int i = 0; i < n; i++) {
            int v = sa[i];
            if (v >= 1 && !ls[v - 1]) {
                sa[buf[s[v - 1]]++] = v - 1;
            }
        }
        std::copy(sum_l.begin(), sum_l.end(), buf.begin());
        for (int i = n - 1; i >= 0; i--) {
            int v = sa[i];
            if (v >= 1 && ls[v - 1]) {
                sa[--buf[s[v - 1] + 1]] = v - 1;
            }
        }
    };
 
    std::vector<int> lms_map(n + 1, -1);
    int m = 0;
    for (int i = 1; i < n; i++) {
        if (!ls[i - 1] && ls[i]) {
            lms_map[i] = m++;
        }
    }
    std::vector<int> lms;
    lms.reserve(m);
    for (int i = 1; i < n; i++) {
        if (!ls[i - 1] && ls[i]) {
            lms.push_back(i);
        }
    }
 
    induce(lms);
 
    if (m) {
        std::vector<int> sorted_lms;
        sorted_lms.reserve(m);
        for (int v : sa) {
            if (lms_map[v] != -1) sorted_lms.push_back(v);
        }
        std::vector<int> rec_s(m);
        int rec_upper = 0;
        rec_s[lms_map[sorted_lms[0]]] = 0;
        for (int i = 1; i < m; i++) {
            int l = sorted_lms[i - 1], r = sorted_lms[i];
            int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;
            int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n;
            bool same = true;
            if (end_l - l != end_r - r) {
                same = false;
            } else {
                while (l < end_l) {
                    if (s[l] != s[r]) {
                        break;
                    }
                    l++;
                    r++;
                }
                if (l == n || s[l] != s[r]) same = false;
            }
            if (!same) rec_upper++;
            rec_s[lms_map[sorted_lms[i]]] = rec_upper;
        }
 
        auto rec_sa =
            sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);
 
        for (int i = 0; i < m; i++) {
            sorted_lms[i] = lms[rec_sa[i]];
        }
        induce(sorted_lms);
    }
    return sa;
}
 
}  // namespace internal
 
std::vector<int> suffix_array(const std::vector<int>& s, int upper) {
    assert(0 <= upper);
    for (int d : s) {
        assert(0 <= d && d <= upper);
    }
    auto sa = internal::sa_is(s, upper);
    return sa;
}
 
template <class T> std::vector<int> suffix_array(const std::vector<T>& s) {
    int n = int(s.size());
    std::vector<int> idx(n);
    iota(idx.begin(), idx.end(), 0);
    sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; });
    std::vector<int> s2(n);
    int now = 0;
    for (int i = 0; i < n; i++) {
        if (i && s[idx[i - 1]] != s[idx[i]]) now++;
        s2[idx[i]] = now;
    }
    return internal::sa_is(s2, now);
}
 
std::vector<int> suffix_array(const std::string& s) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return internal::sa_is(s2, 255);
}
 
template <class T>
std::vector<int> lcp_array(const std::vector<T>& s,
                           const std::vector<int>& sa) {
    int n = int(s.size());
    assert(n >= 1);
    std::vector<int> rnk(n);
    for (int i = 0; i < n; i++) {
        rnk[sa[i]] = i;
    }
    std::vector<int> lcp(n - 1);
    int h = 0;
    for (int i = 0; i < n; i++) {
        if (h > 0) h--;
        if (rnk[i] == 0) continue;
        int j = sa[rnk[i] - 1];
        for (; j + h < n && i + h < n; h++) {
            if (s[j + h] != s[i + h]) break;
        }
        lcp[rnk[i] - 1] = h;
    }
    return lcp;
}
 
std::vector<int> lcp_array(const std::string& s, const std::vector<int>& sa) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return lcp_array(s2, sa);
}
 
template <class T> std::vector<int> z_algorithm(const std::vector<T>& s) {
    int n = int(s.size());
    if (n == 0) return {};
    std::vector<int> z(n);
    z[0] = 0;
    for (int i = 1, j = 0; i < n; i++) {
        int& k = z[i];
        k = (j + z[j] <= i) ? 0 : std::min(j + z[j] - i, z[i - j]);
        while (i + k < n && s[k] == s[i + k]) k++;
        if (j + z[j] < i + z[i]) j = i;
    }
    z[0] = n;
    return z;
}
 
std::vector<int> z_algorithm(const std::string& s) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return z_algorithm(s2);
}
 
}  // namespace atcoder
namespace atcoder {
 
struct two_sat {
  public:
    two_sat() : _n(0), scc(0) {}
    explicit two_sat(int n) : _n(n), _answer(n), scc(2 * n) {}
 
    void add_clause(int i, bool f, int j, bool g) {
        assert(0 <= i && i < _n);
        assert(0 <= j && j < _n);
        scc.add_edge(2 * i + (f ? 0 : 1), 2 * j + (g ? 1 : 0));
        scc.add_edge(2 * j + (g ? 0 : 1), 2 * i + (f ? 1 : 0));
    }
    bool satisfiable() {
        auto id = scc.scc_ids().second;
        for (int i = 0; i < _n; i++) {
            if (id[2 * i] == id[2 * i + 1]) return false;
            _answer[i] = id[2 * i] < id[2 * i + 1];
        }
        return true;
    }
    std::vector<bool> answer() { return _answer; }
 
  private:
    int _n;
    std::vector<bool> _answer;
    internal::scc_graph scc;
};
 
}  // namespace atcoder



//——————————————————Atcoder Library———————————————————






#define endl "\n"              //←これ
using namespace atcoder;
#define rep(i,n) for(ll i=0; i<(ll)(n); i++)
#define repo(i,n) for(ll i=1; i<(ll)(n); i++)
#define pb push_back
#define np next_permutation
#define fi first
#define se second
#define all(x) (x).begin(),(x).end()
#define lb(v,x) (lower_bound(v.begin(),v.end(),x)-v.begin())
#define ub(v,x) (upper_bound(v.begin(),v.end(),x)-v.begin())
#define cou(x) __builtin_popcountll(x)
const ld pi=acos(-1.0);
const ll INF = 1LL<<61;
template<class T>bool chmax(T &a, const T &b) { 
  if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) {
  if (b<a) { a=b; return 1; } return 0; }
ll gcd(ll x, ll y) { return y ? gcd(y, x % y) : x; }
ll lcm(ll x, ll y) { return x / gcd(x, y) * y; }

vector<ll> vl(ll n,ll x){
  vector<ll> re(n,x);
  return re;}
vector<vector<ll>> vl(ll n, ll m,ll x){
  vector<vector<ll>> re(n,vector<ll>(m,x));
  return re;}
vector<vector<vector<ll>>> vl(ll n, ll m, ll l,ll x){
  vector<vector<vector<ll>>> re(n,vector<vector<ll>>(m,vector<ll>(l,x)));
  return re;}

template<class T>void out(T x) {cout << x << endl;}
template<class T>void out(T x,T y) {cout << x << " " << y << endl;}
template<class T>void out(T x,T y,T z) {cout << x << " " << y << " " << z << endl;}
template<class T>void out(T x,T y,T z,T a) {cout << x << " " << y << " " << z << " " << a << endl;}
template<class T>void out(pair<T,T> p) {cout << p.fi << " " << p.se << endl;}

template<class T>void vout(vector<T> &v) {
  if(v.size() > 0) { for(auto it = v.begin(); it < v.end(); it++) {
	  cout << *it;
	  if(it != v.end() - 1) cout << " ";
  } } cout << endl; }

template<class T>void vout(vector<vector<T>> &v) {
  if(v.size() > 0) { for(auto it = v.begin(); it < v.end(); it++) {
  vout(*it); } }
}

template<class T>void vout(vector<pair<T,T>> &v) {
  if(v.size() > 0) { for(auto it = v.begin(); it < v.end(); it++) {
  out(*it); } }
}

template<class T>void rev(vector<T> &v) {sort(v.rbegin(),v.rend());}

vector<string> YES={"NO","YES"};
vector<string> Yes={"No","Yes"};
vector<string> yes={"no","yes"};
vector<string> POS={"IMPOSSIBLE","POSSIBLE"};
vector<string> Pos={"Impossible","Possible"};
vector<string> pos={"impossible","possible"};
vector<string> TAO={"TAKAHASHI","AOKI"};
vector<string> Tao={"Takahashi","Aoki"};
vector<string> tao={"takahashi","aoki"};
vector<string> YAY={":(","YAY!"};
vector<string> Yay={":(","Yay!"};
vector<string> yay={":(","yay!"};


//———————————————tento 転倒数—————————————————
  ll tento(vector<ll>v){
    ll n=v.size();
    vector<ll> v2(n);
    vector<pll> vp(n);
    rep(i,n) vp[i]={v[i],i};
    sort(all(vp));
    rep(i,n) v2[vp[i].se]=i;
    fenwick_tree<ll> bit(n);
    ll re=0;
    rep(i,n){
      re+=i-bit.sum(0,v2[i]+1);
      bit.add(v2[i], 1);      
    }
    return re;
  }
//———————————————————————————————————————————————

//———————————————LIS　最長増加部分列—————————————————
ll lis(vector<ll> &v) {
  ll n=v.size();
  vector<ll> dp(n,INF);
  rep(i,n) {
    ll x=lb(dp,v[i]);
    dp[x] = v[i];
  }
  return lb(dp,INF);
}
//———————————————————————————————————————————————

//————————————距離/面積/内接円半径/外接円中心半径————————————————————
ld kyo(ld x1,ld y1,ld x2,ld y2){
  ld sx=x1-x2;
  ld sy=y1-y2;
  ld re=sqrt(sx*sx+sy*sy);
  return re;
}
ld kyo(ld x,ld y){
  ld re=sqrt(x*x+y*y);
  return re;
}

ld men(ld x1,ld y1,ld x2,ld y2,ld x3,ld y3){
  ld vx=x2-x1;
  ld vy=y2-y1;
  ld vx2=x3-x1;
  ld vy2=y3-y1;
  ld re=abs(vx*vy2-vy*vx2)/2.0;
  return re;
}
ld men(ld a,ld b,ld c){
  if(a<=0||b<=0||c<=0) return 0;
  ld s=(a+b+c)/2.0;
  if(s-a<=0||s-b<=0||s-c<=0) return 0;
  ld re=sqrt(s*(s-a)*(s-b)*(s-c));
  return re;
}

ld nai(ld x1,ld y1,ld x2,ld y2,ld x3,ld y3){
  ld a=kyo(x1,y1,x2,y2);
  ld b=kyo(x1,y1,x3,y3);
  ld c=kyo(x2,y2,x3,y3);
  if(a+b+c==0) return 0;
  ld re=(2*men(x1,y1,x2,y2,x3,y3))/(a+b+c);
  return re;
}

pair<pdd,ld> gai(ld x1,ld y1,ld x2,ld y2,ld x3,ld y3){
  if((x2-x1)*(y3-y1)==(x3-x1)*(y2-y1)) return {{0,0},-1};
  ld cx=(x2*x2-x1*x1+y2*y2-y1*y1)*(y3-y1)-(x3*x3-x1*x1+y3*y3-y1*y1)*(y2-y1);
  cx/=((x2-x1)*(y3-y1)-(x3-x1)*(y2-y1))*2.0;
  ld cy=(x2*x2-x1*x1+y2*y2-y1*y1)*(x3-x1)-(x3*x3-x1*x1+y3*y3-y1*y1)*(x2-x1);
  cy/=((x3-x1)*(y2-y1)-(x2-x1)*(y3-y1))*2.0;
  ld r=kyo(x1,y1,cx,cy);
  return {{cx,cy},r};
}
//——————————————————————————————————————

//ベクター入力
  vector<ll> pin(ll n){
    vector<ll> re(n);
    rep(i,n) cin>>re[i];
    return re;
  }
//ベクター入力 -1
  vector<ll> hin(ll n){
    vector<ll> re(n);
    rep(i,n){
      cin>>re[i];
      re[i]--;
    }
    return re;
  }

//二次元ベクター入力
  vector<vector<ll>> ppin(ll h,ll w){
    vector<vector<ll>> re(h,vector<ll>(w));
    rep(i,h) rep(j,w) cin>>re[i][j];
    return re;
  }
//二次元ベクター入力 -1
  vector<vector<ll>> hhin(ll h,ll w){
    vector<vector<ll>> re(h,vector<ll>(w));
    rep(i,h) rep(j,w){
      cin>>re[i][j];
      re[i][j]--;
    }
    return re;
  }


//ペア入力
  vector<pll> pain(ll n){
    vector<pll> re(n);
    rep(i,n){
      ll a,b;
      cin>>a>>b;
      re[i]={a,b};
    }
    return re;
  }
//ペア入力 -1
  vector<pll> hain(ll n){
    vector<pll> re(n);
    rep(i,n){
      ll a,b;
      cin>>a>>b;
      a--;b--;
      re[i]={a,b};
    }
    return re;
  }

//ストリング入力
  vector<string> stin(ll n){
    vector<string> re(n);
    rep(i,n) cin>>re[i];
    return re;
  }

//グラフ入力
  vector<vector<ll>> gin(ll n, ll m){
    vector<vector<ll>> re(n);
    rep(i,m){
      ll a,b;
      cin>>a>>b;
      a--;b--;
      re[a].pb(b);
      re[b].pb(a);
    }
    return re;
  }
//グラフdist
  vector<ll> gdis(vector<vector<ll>> &g, ll st){
    ll n=g.size();
    vector<ll> dist(n,INF);
    queue<ll> que;
    dist[st]=0;
    que.push(st);
    while(!que.empty()){
      ll x=que.front();
      que.pop();
      for(ll nx:g[x]){
        if(dist[nx]!=INF) continue;
        dist[nx]=dist[x]+1;
        que.push(nx);
      }
    }
    return dist;
  }

//グラフ距離入力
  vector<vector<pll>> ggin(ll n, ll m){
    vector<vector<pll>> re(n);
    rep(i,m){
      ll a,b,c;
      cin>>a>>b>>c;
      a--;b--;
      re[a].pb({b,c});
      re[b].pb({a,c});
    }
    return re;
  }
//グラフ距離dist
  vector<ll> gdis(vector<vector<pll>> &g, ll st){
    ll n=g.size();
    vector<ll> dist(n,INF);
    priority_queue<pll,vector<pll>,greater<pll>> que;
    dist[st]=0;
    que.push({0,st});
    while(!que.empty()){
      pll z=que.top();
      que.pop();
      ll x=z.se;
      if(dist[x]!=z.fi) continue;
      for(pll nz:g[x]){
        ll nx=nz.fi;
        ll ny=nz.se;
        if(dist[nx]<=dist[x]+ny) continue;
        dist[nx]=dist[x]+ny;
        que.push({dist[nx],nx});
      }
    }
    return dist;
  }

//intの最大値2147483647 ≒ 2×10^9
//long longの最大値9223372036854775807 ≒ 9×10^18
//実行時間制約2秒では２×10^8回くらいまで計算できる
//「#define endl "\n"」はインタラクティブで消す！！！

using mint = modint998244353;
//using mint = modint1000000007;
//using mint = modint;
//下でmodint::set_mod(m);

void out(mint &x) {out(x.val());}
void out(mint &x,mint &y) {out(x.val(),y.val());}
void out(mint &x,mint &y,mint &z) {out(x.val(),y.val(),z.val());}
void out(mint &x,mint &y,mint &z,mint &a) {out(x.val(),y.val(),z.val(),a.val());}
vector<mint> vm(ll n){
  vector<mint> re(n,0);
  return re;}
vector<vector<mint>> vm(ll n, ll m){
  vector<vector<mint>> re(n,vector<mint>(m,0));
  return re;}
vector<vector<vector<mint>>> vm(ll n, ll m, ll l){
  vector<vector<vector<mint>>> re(n,vector<vector<mint>>(m,vector<mint>(l,0)));
  return re;}

void vout(vector<mint> &v){
  ll n=v.size();
  rep(i,n-1) cout<<v[i].val()<<" ";
  cout<<v[n-1].val()<<endl;
}
void vout(vector<vector<mint>> &v){
  ll n=v.size();
  if(n>0) rep(i,n) vout(v[i]);
}

vector<ll> vx={1,-1,0,0,1,-1,1,-1,0};
vector<ll> vy={0,0,1,-1,1,-1,-1,1,0};

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);

  mint ans=1;
  rep(i,3){
    ll a;
    cin>>a;
    ans*=a;
    ans*=a+1;
    ans/=2;
  }
  out(ans);
}