#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define forr(x,arr) for(auto&& x:arr) #define _overload3(_1,_2,_3,name,...) name #define _rep2(i,n) _rep3(i,0,n) #define _rep3(i,a,b) for(int i=int(a);i=int(a);i--) #define rrep(...) _overload3(__VA_ARGS__,_rrep3,_rrep2,)(__VA_ARGS__) #define all(x) (x).begin(),(x).end() #define bit(n) (1LL<<(n)) #define sz(x) ((int)(x).size()) #define TEN(n) ((ll)(1e##n)) #define fst first #define snd second string DBG_DLM(int &i){return(i++==0?"":", ");} #define DBG_B(exp){int i=0;os<<"{";{exp;}os<<"}";return os;} templateostream&operator<<(ostream&os,vectorv); templateostream&operator<<(ostream&os,setv); templateostream&operator<<(ostream&os,queueq); templateostream&operator<<(ostream&os,priority_queueq); templateostream&operator<<(ostream&os,pairp); templateostream&operator<<(ostream&os,mapmp); templateostream&operator<<(ostream&os,unordered_mapmp); templatevoid DBG(ostream&os,TPL t){} templatevoid DBG(ostream&os,TPL t){os<<(I==0?"":", ")<(t);DBG(os,t);} templatevoid DBG(ostream&os,pairp,string delim){os<<"("<ostream&operator<<(ostream&os,tuplet){os<<"(";DBG<0,tuple,Ts...>(os,t);os<<")";return os;} templateostream&operator<<(ostream&os,pairp){DBG(os,p,", ");return os;} templateostream&operator<<(ostream&os,vectorv){DBG_B(forr(t,v){os<ostream&operator<<(ostream&os,sets){DBG_B(forr(t,s){os<ostream&operator<<(ostream&os,queueq){DBG_B(for(;q.size();q.pop()){os<ostream&operator<<(ostream&os,priority_queueq){DBG_B(for(;q.size();q.pop()){os<ostream&operator<<(ostream&os,mapm){DBG_B(forr(p,m){os<");});} templateostream&operator<<(ostream&os,unordered_mapm){DBG_B(forr(p,m){os<");});} #define DBG_OVERLOAD(_1,_2,_3,_4,_5,_6,macro_name,...)macro_name #define DBG_LINE(){char s[99];sprintf(s,"line:%3d | ",__LINE__);cerr<;using pll=pair;using pil=pair;using pli=pair; using vs=vector;using vvs=vector;using vvvs=vector; using vb=vector;using vvb=vector;using vvvb=vector; using vi=vector;using vvi=vector;using vvvi=vector; using vl=vector;using vvl=vector;using vvvl=vector; using vd=vector;using vvd=vector;using vvvd=vector; using vpii=vector;using vvpii=vector;using vvvpii=vector; templatebool amax(A&a,const B&b){return b>a?a=b,1:0;} templatebool amin(A&a,const B&b){return b>l;return l;} string rs(){string s;cin>>s;return s;} template struct ConvexHullTrickAddQueryMonotone { deque> L; static bool cmp(const T l, const T r) { return getMin ? l >= r : l <= r; } static bool checkRemove(const pair &a, const pair &b, const pair &c) { if (getMin) return (b.first - a.first) * (c.second - b.second) >= (b.second - a.second) * (c.first - b.first); else return (b.second - a.second) * (a.first - c.first) >= (c.second - a.second) * (a.first - b.first); } static T f(const pair &a, const T x) { return a.first * x + a.second; } int size() const { return L.size(); } bool empty() const { return L.empty(); } void add(const T a, const T b) { pair line(a, b); while (!L.empty() && L.back().first == a) { line.second = getMin ? min(line.second, L.back().second) : max(line.second, L.back().second); L.pop_back(); } while (L.size() >= 2 && checkRemove(L[L.size()-2], L[L.size()-1], line)) L.pop_back(); L.emplace_back(line); } T get(const T x) { if (getMonotone) { while (L.size() >= 2 && cmp(f(L[0], x), f(L[1], x))) L.pop_front(); return f(L.front(), x); } else { int low = -1, high = (int)L.size() - 1; while (high - low > 1) { int mid = (low + high) >> 1; if (cmp(f(L[mid], x), f(L[mid + 1], x))) low = mid; else high = mid; } return f(L[high], x); } } }; void Main() { int n = ri(); ll a = ri(), b = ri(), w = ri(); vector D(n); rep(i, n) D[i] = ri(); ConvexHullTrickAddQueryMonotone cht; vl dp(n+1, 1e18); dp[0] = 0; cht.add(0, 0); rep(i, 1, n+1) { dp[i] = cht.get(i) - a * (i-1) + i * (i-1LL) / 2 * b + D[i-1]; cht.add(-i*b, dp[i]+i*a+i*(i+1LL)/2*b); } ll ans = 1e18; rep(t, n+1) { amin(ans, dp[t] - (n+1-t-1) * a + (n+1-t) * (n+1-t-1LL) / 2 * b); } cout << w + ans << endl; } signed main() { cin.tie(nullptr); ios::sync_with_stdio(false); Main(); return 0; }