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.
#include <bits/stdc++.h>
int n;
long long s[100007], f[100007][5], ma, a[10];
using namespace std;
int main() {
  scanf("%d%lld%lld%lld", &n, &a[1], &a[2], &a[3]);
  for (int i = 1; i <= n; i++) scanf("%lld", &s[i]);
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= 3; j++) f[i][j] = -1e18 * 4;
  f[1][1] = s[1] * a[1];
  for (int i = 2; i <= n; i++) f[i][1] = max(s[i] * a[1], f[i - 1][1]);
  f[1][2] = f[1][1] + s[1] * a[2];
  for (int i = 2; i <= n; i++)
    f[i][2] = max(f[i][1] + s[i] * a[2], f[i - 1][2]);
  f[1][3] = f[1][2] + s[1] * a[3];
  ma = f[1][3];
  for (int i = 2; i <= n; i++) {
    f[i][3] = max(f[i][2] + s[i] * a[3], f[i - 1][3]);
    ma = max(ma, f[i][3]);
  }
  printf("%lld\n", ma);
}
