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·ai + q·aj + r·ak for given p, q, r and array a1, a2, ... an 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, ... an ( - 109 ≤ ai ≤ 109).

Output

Output a single integer the maximum value of p·ai + q·aj + r·ak that can be obtained provided 1 ≤ i ≤ j ≤ k ≤ n.

Examples

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.
import math;
import sys;
lineno=0;
for line in sys.stdin:
	if lineno==0:
		n,p,q,r = map(long, line.split());
		lineno=1;
	else:
		a = list(map(long, line.split()));

dp_a=[];
dp_b=[];
dp_c=[];
for i in range(n):
 dp_a.append(1);
 dp_b.append(1);
 dp_c.append(1);

dp_a[0]=p*a[0];
dp_b[0]=q*a[0]+p*a[0];
dp_c[0]=(p+q+r)*a[0];

for i in range(n-1):
	i=i+1;
	dp_c[i]=max(dp_c[i-1],(p+q+r)*a[i]);
	dp_c[i]=max(dp_c[i],dp_b[i-1]+(r)*a[i]);
	dp_c[i]=max(dp_c[i],dp_a[i-1]+(q+r)*a[i]);
	dp_b[i]=max(dp_b[i-1],(p+q)*a[i]);
	dp_b[i]=max(dp_b[i],dp_a[i-1]+(q)*a[i]);
	dp_a[i]=max(dp_a[i-1],p*a[i]);
	i=i-1;

print dp_c[n-1];