#include using namespace std; #define GET_MACRO(_1, _2, _3, NAME, ...) NAME #define _repl(i,a,b) for(int i=(int)(a);i<(int)(b);i++) #define _rep(i,n) _repl(i,0,n) #define rep(...) GET_MACRO(__VA_ARGS__, _repl, _rep)(__VA_ARGS__) #define mp(a,b) make_pair((a),(b)) #define pb(a) push_back((a)) #define all(x) (x).begin(),(x).end() #define uniq(x) sort(all(x)),(x).erase(unique(all(x)),end(x)) #define fi first #define se second #define dbg(...) _dbg(#__VA_ARGS__, __VA_ARGS__) void _dbg(string){cout< void _dbg(string s,H h,T... t){int l=s.find(',');cout< ostream& operator<<(ostream &o, const pair &p){o<<"("< ostream& operator<<(ostream &o, const vector &v){o<<"[";for(T t:v){o< class ConvexHullTrick { private: vector> data; int pt; bool check(pair &p){ int s = data.size(); return (U)(data[s-1].fi-data[s-2].fi)*(p.se-data[s-1].se) < (U)(data[s-1].se-data[s-2].se)*(p.fi-data[s-1].fi); } public: ConvexHullTrick(){ pt = 0; } // additions of 'a' shold be NON-INCREASING void add(T a, T b){ auto p = mp(a,b); while(data.size()>=2 && !check(p)) data.pop_back(); data.push_back(p); } inline T val(int i, T x) { return data[i].fi*x + data[i].se; } // queries shold be NON-DECREASING T query(T x){ pt = min(data.size()-1, pt); while(pt+1 < (int)data.size() && val(pt, x) >= val(pt+1, x)) pt++; return val(pt, x); } }; int main(){ long n,a,b,w; cin>>n>>a>>b>>w; vector d(n); rep(i,n) cin>>d[i]; vector dp(n+1, 0); dp[0] = w; ConvexHullTrick cht; cht.add(b,w); rep(i,n){ dp[i+1] = cht.query(i) - i*a + b*i*(i-1)/2 + d[i]; cht.add(-b*i, dp[i+1] + (i+1)*a + b*i*(i+1)/2); } long ans = dp[n]; rep(i,n) ans = min(ans, dp[i] -a*(n-i) + b*(n-i)*(n-i+1)/2); cout << ans << endl; return 0; }