#include #include using namespace std; #define rep(i,n) for(long long i = 0; i < (long long)(n); i++) #define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++) #define pb push_back #define all(x) (x).begin(), (x).end() #define fi first #define se second #define mt make_tuple #define mp make_pair #define ZERO(a) memset(a,0,sizeof(a)) template bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); } template bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } #define exists find_if #define forall all_of using ll = long long; using vll = vector; using vvll = vector; using P = pair; using ld = long double; using vld = vector; using vi = vector; using vvi = vector; vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; } inline void input(int &v){ v=0;char c=0;int p=1; while(c<'0' || c>'9'){if(c=='-')p=-1;c=getchar();} while(c>='0' && c<='9'){v=(v<<3)+(v<<1)+c-'0';c=getchar();} v*=p; } template ostream &operator<<(ostream &o, const pair &v) { o << "(" << v.first << ", " << v.second << ")"; return o; } template struct seq{}; template struct gen_seq : gen_seq{}; template struct gen_seq<0, Is...> : seq{}; template void print_tuple(basic_ostream& os, Tuple const& t, seq){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get(t)), 0)...}; } template auto operator<<(basic_ostream& os, tuple const& t) -> basic_ostream& { os << "("; print_tuple(os, t, gen_seq()); return os << ")"; } ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; o << endl; } return o; } template ostream &operator<<(ostream &o, const vector &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const set &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const unordered_set &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const map &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const unordered_map &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]"; return o; } vector range(const int x, const int y) { vector v(y - x + 1); iota(v.begin(), v.end(), x); return v; } template istream& operator>>(istream& i, vector& o) { rep(j, o.size()) i >> o[j]; return i;} string bits_to_string(ll input, ll n=64) { string s; rep(i, n) s += '0' + !!(input & (1ll << i)); reverse(all(s)); return s; } template ostream &operator<<(ostream &o, const priority_queue &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.top(); tmp.pop(); o << x << " ";} o << endl; return o; } template unordered_map counter(vector vec){unordered_map ret; for (auto&& x : vec) ret[x]++; return ret;}; string substr(string s, P x) {return s.substr(x.fi, x.se - x.fi); } void vizGraph(vvll& g, int mode = 0, string filename = "out.png") { ofstream ofs("./out.dot"); ofs << "digraph graph_name {" << endl; set

memo; rep(i, g.size()) rep(j, g[i].size()) { if (mode && (memo.count(P(i, g[i][j])) || memo.count(P(g[i][j], i)))) continue; memo.insert(P(i, g[i][j])); ofs << " " << i << " -> " << g[i][j] << (mode ? " [arrowhead = none]" : "")<< endl; } ofs << "}" << endl; ofs.close(); system(((string)"dot -T png out.dot >" + filename).c_str()); } size_t random_seed; namespace std { using argument_type = P; template<> struct hash { size_t operator()(argument_type const& x) const { size_t seed = random_seed; seed ^= hash{}(x.fi); seed ^= (hash{}(x.se) << 1); return seed; } }; }; // hash for various class namespace myhash{ const int Bsizes[]={3,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77,81}; const int xor_nums[]={0x100007d1,0x5ff049c9,0x14560859,0x07087fef,0x3e277d49,0x4dba1f17,0x709c5988,0x05904258,0x1aa71872,0x238819b3,0x7b002bb7,0x1cf91302,0x0012290a,0x1083576b,0x76473e49,0x3d86295b,0x20536814,0x08634f4d,0x115405e8,0x0e6359f2}; const int hash_key=xor_nums[rand()%20]; const int mod_key=xor_nums[rand()%20]; template struct myhash{ std::size_t operator()(const T& val) const { return (hash{}(val)%mod_key)^hash_key; } }; }; template class uset:public std::unordered_set> { using SET=std::unordered_set>; public: uset():SET(){SET::rehash(myhash::Bsizes[rand()%20]);} }; uint32_t randxor() { static uint32_t x=1+(uint32_t)random_seed,y=362436069,z=521288629,w=88675123; uint32_t t; t=(x^(x<<11));x=y;y=z;z=w; return( w=(w^(w>>19))^(t^(t>>8)) ); } struct timeval start; double sec() { struct timeval tv; gettimeofday(&tv, NULL); return (tv.tv_sec - start.tv_sec) + (tv.tv_usec - start.tv_usec) * 1e-6; } struct init_{init_(){ gettimeofday(&start, NULL); ios::sync_with_stdio(false); cin.tie(0); struct timeval myTime; struct tm *time_st; gettimeofday(&myTime, NULL); time_st = localtime(&myTime.tv_sec); srand(myTime.tv_usec); random_seed = RAND_MAX / 2 + rand() / 2; }} init__; #define rand randxor static const double EPS = 1e-14; static const long long INF = 1e18; static const long long mo = 1e9+7; #define ldout fixed << setprecision(40) #if 1 // Incremental Convex Hull Trick // N<=1000000に注意 // // 追加ax+bのaが単調減少 O(1) // 質問クエリf(x)のxが単調増加 O(1) namespace CHT{ using TYPE=long long; pair mem[1000000]; template inline bool is_minimam(T a1,T b1,T a2,T b2,T a3,T b3){return (a2-a1)*(b3-b2)>=(b2-b1)*(a3-a2);} template inline bool is_maximam(T a1,T b1,T a2,T b2,T a3,T b3){return is_minimam(-a1,-b1,-a2,-b2,-a3,-b3);} template inline bool check(pair L1,pair L2,pair L3){ return is_minimam(L1.first,L1.second,L2.first,L2.second,L3.first,L3.second); } template inline T calc(pair L,T now){ return L.first*now+L.second; } }; template ostream& operator<<(ostream& os,pair t){ os <<"("<< t.first << " "< class convex_hull_trick{ pair *deque; int s,t; public: convex_hull_trick(pair *mem):deque(mem),s(0),t(0){} convex_hull_trick():convex_hull_trick(CHT::mem){} void add(T a,T b){ auto L=make_pair(a,b); while(s+1=CHT::calc(deque[s+1],now))s++; return CHT::calc(deque[s],now); } void pop(){ while(s+1=CHT::calc(deque[s+1]))s++; } }; ll dp[300010]; int main(void) { ll n, a, b, w; cin >> n >> a >> b >> w; vll d(n); cin >> d; repi(i, 1, n+10) dp[i] = INF; dp[0] = 2ll*w; convex_hull_trick c; // 集めるDP repi(i, 1, n+1) { /* rep(k, i) chmin(dp[i], i*(-2*k*b)+(dp[k]+b*k*k+k*b+2*k*a)); dp[i] += i*i*b-i*b-2*i*a+2*a+2*d[i-1]; */ ll k = i-1; c.add(-2*k*b, dp[k]+b*k*k+k*b+2*k*a); dp[i] = c.get(i); dp[i] += i*i*b-i*b-2*i*a+2*a+2*d[i-1]; } ll ret = INF; rep(k, n+1) { chmin(ret, dp[n-k]+k*(k+1)*b-k*a*2ll); } cout << ret / 2 << endl; return 0; } #else ll dp[300010]; int main(void) { ll n, a, b, w; cin >> n >> a >> b >> w; vll d(n); cin >> d; repi(i, 1, n+10) dp[i] = INF; dp[0] = 2ll*w; // 集めるDP repi(i, 1, n+1) { rep(k, i) { chmin(dp[i], dp[i-k-1] + k*(k+1ll)*b-k*a*2ll+d[i-1]*2ll); } } double ret = INF; rep(k, n+1) { chmin(ret, dp[n-k]+k*(k+1)*b-k*a*2ll); } cout << ret / 2 << endl; return 0; } #endif