#!/usr/bin/ruby def is_minimam(a1,b1,a2,b2,a3,b3) (a2-a1)*(b3-b2)>=(b2-b1)*(a3-a2) end def is_maximam(a1,b1,a2,b2,a3,b3) is_minimam(-a1,-b1,-a2,-b2,-a3,-b3) end def check(l1,l2,l3) is_minimam(l1[0],l1[1],l2[0],l2[1],l3[0],l3[1]) end def calc(l,now) l[0]*now+l[1] end class ConvexHullTrick def initialize @deque=100000.times.map{[0,0]} @s=0 @t=0 end def add(a,b) l=[a,b] while @s+1<@t&&check(@deque[@t-2],@deque[@t-1],l) @t-=1 end @deque[@t]=l @t+=1 end def get(now) while @s+1<@t&&calc(@deque[@s],now)>=calc(@deque[@s+1],now) @s+=1 end calc(@deque[@s],now) end end n,a,b,w=gets.split.map(&:to_i) d=gets.split.map(&:to_i) deq=ConvexHullTrick.new dp=[Float::INFINITY]*(n+1) dp[0]=w deq.add( - 0 * b,dp[0] + 0 * a + b * 0 * (0 - 1) / 2) n.times{|i| dp[i + 1] = d[i] - i * a + ( b * i * (i + 1)) / 2 + deq.get(i) deq.add( - (i + 1) * b , dp[i + 1] + (i + 1) * a + ( b * (i + 1) * i) / 2) } res=Float::INFINITY (n+1).times{|i| res=[res,dp[i] - a * (n -i) + b * (n - i) * (n - i + 1) / 2].min } p res