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>
using namespace std;
int main() {
  long long int x[3];
  int i, n, j;
  cin >> n >> x[0] >> x[1] >> x[2];
  long long int arr[n];
  long long int mtx[4][n + 1];
  for (i = 0; i < n; i++) cin >> arr[i];
  for (i = 0; i <= n; i++) mtx[0][i] = 0;
  for (i = 1; i < 4; i++) mtx[i][0] = LLONG_MIN;
  for (i = 1; i <= 3; i++) {
    for (j = 1; j <= n; j++)
      mtx[i][j] = max(mtx[i][j - 1], mtx[i - 1][j] + x[i - 1] * arr[j - 1]);
  }
  cout << mtx[3][n];
  return 0;
}
