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 a₁, a₂, ... 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.

Input

First line of input contains 4 integers n, p, q, r ( - 10⁹ ≤ p, q, r ≤ 10⁹, 1 ≤ n ≤ 10⁵).

Next line of input contains n space separated integers a₁, a₂, ... a_n ( - 10⁹ ≤ a_i ≤ 10⁹).

Output

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.

Example

Input

5 1 2 3 1 2 3 4 5

Output

30

Input

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

Output

12

Note

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.

题解：注意顺序是一定的，i<=j<=k，所以可以枚举中间值j，然后用两个数组分别存第一项的前缀最大值，第三项的后缀最大值，最后加起来遍历一遍就行了。

1 #include
       
         2 using namespace std; 3 typedef long long ll; 4  5 const int maxn=1e5+5; 6  7 ll n,p,q,r; 8 ll a[maxn],b[maxn],c[maxn]; 9 10 int main()11 {   cin>>n>>p>>q>>r;12     ll temp;13     for(int i=1;i<=n;i++){14         cin>>temp;15         a[i]=p*temp;16         b[i]=q*temp;17         c[i]=r*temp;18     }    19     temp=a[1];20     for(int i=1;i<=n;i++){21         temp=max(temp,a[i]);22         a[i]=temp;23     }24     temp=c[n];25     for(int i=n;i>=1;i--){26         temp=max(temp,c[i]);27         c[i]=temp;28     }29     temp=a[1]+b[1]+c[1];30     for(int i=1;i<=n;i++) temp=max(temp,a[i]+b[i]+c[i]);31     cout<
        
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