#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 DequeV { vector arr; size_t head = 0, tail = 0; void clear() { head = tail = 0; arr.clear();} int size() const { return tail - head; } bool empty() const { return tail == head; } T front() const { return arr[head]; } T back() const { return arr[tail - 1]; } T front(int i) const { return arr[head + i]; } T back(int i) const { return arr[tail - 1 - i]; } void pop_front() { head++; } void pop_back() { tail--; } void push_back(T v) { if (tail < arr.size()) arr[tail++] = v; else arr.push_back(v), tail++; } }; templateostream&operator<<(ostream&os,DequeVq){DBG_B(for(;q.size();q.pop_front()){os< struct ConvecHullTrick { DequeV > lines; bool isMonotonicX; function comp; ConvecHullTrick(bool flagX = false, function compFunc = [](T l, T r) {return l >= r; }) :isMonotonicX(flagX), comp(compFunc) { lines.push_back(make_pair(0, 0)); }; bool check(pair l1, pair l2, pair l3) { if (l1 < l3) swap(l1, l3); return (l3.second - l2.second) * (l2.first - l1.first) >= (l2.second - l1.second) * (l3.first - l2.first); } void add(T a, T b) { pair line(a, b); while (lines.size() >= 2 && check(lines.back(1), lines.back(), line)) lines.pop_back(); lines.push_back(line); } T f(int i, T x) { return lines.front(i).first * x + lines.front(i).second; } T f(pair line, T x) { return line.first * x + line.second; } T get(T x) { if (isMonotonicX) { while (lines.size() >= 2 && comp(f(lines.front(), x), f(lines.front(1), x))) lines.pop_front(); return f(lines.front(), x); } else { int low = -1, high = lines.size() - 1; while (high - low > 1) { int mid = (high + low) / 2; (comp(f(mid, x), f(mid + 1, x)) ? low : high) = mid; } return f(high, x); } } }; void Main() { int n = ri(); ll a = ri(), b = ri(), w = ri(); vector D(n); rep(i, n) D[i] = ri(); ConvecHullTrick cht(true); vl dp(n+1, 1e18); dp[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; }