Marvolo Gaunt's Ring

题意翻译

给了三个数: $p,q,r(-1e9<=p,q,r<=1e9)$ 然后给了n个数$a_1,a_2...a_n(-1e9<=a_i<=1e9)$ 求找出三个数$a_i,a_j,a_k(1<=i<=j<=k<=n)$使得$p\times a_i+q\times a_j+r\times a_k$最大。

题目描述

Professor Dumbledore is helping Harry destroy the Horcruxes. He went to Gaunt Shack as he suspected a Horcrux to be present there. He saw Marvolo Gaunt's Ring and identified it as a Horcrux. Although he destroyed it, he is still affected by its curse. Professor Snape is helping Dumbledore remove the curse. For this, he wants to give Dumbledore exactly $ x $ drops of the potion he made. Value of $ x $ is calculated as maximum of $ p·a_{i}+q·a_{j}+r·a_{k} $ for given $ p,q,r $ and array $ a_{1},a_{2},...\ a_{n} $ such that $ 1<=i<=j<=k<=n $ . Help Snape find the value of $ x $ . Do note that the value of $ x $ may be negative.

输入输出格式

输入格式

First line of input contains $ 4 $ integers $ n,p,q,r $ ( $ -10^{9}<=p,q,r<=10^{9},1<=n<=10^{5} $ ). Next line of input contains $ n $ space separated integers $ a_{1},a_{2},...\ a_{n} $ ( $ -10^{9}<=a_{i}<=10^{9} $ ).

输出格式

Output a single integer the maximum value of $ p·a_{i}+q·a_{j}+r·a_{k} $ that can be obtained provided $ 1<=i<=j<=k<=n $ .

输入输出样例

输入样例 #1

5 1 2 3
1 2 3 4 5

输出样例 #1

30

输入样例 #2

5 1 2 -3
-1 -2 -3 -4 -5

输出样例 #2

12

说明

In the first sample case, we can take $ i=j=k=5 $ , thus making the answer as $ 1·5+2·5+3·5=30 $ . In second sample case, selecting $ i=j=1 $ and $ k=5 $ gives the answer $ 12 $ .

题意翻译

给了三个数: $p,q,r(-1e9<=p,q,r<=1e9)$ 然后给了n个数$a_1,a_2...a_n(-1e9<=a_i<=1e9)$ 求找出三个数$a_i,a_j,a_k(1<=i<=j<=k<=n)$使得$p\times a_i+q\times a_j+r\times a_k$最大。