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;
long long ar[500010], in[500010], dp[500010][4], n, hoise[500010][4];
long long rec(int p, int t) {
  if (t == 3) return 0;
  if (p == n) return (long long)-3000000000000000100;
  if (hoise[p][t] != -1) return dp[p][t];
  hoise[p][t] = 1;
  return dp[p][t] = max(ar[p] * in[t] + rec(p, t + 1), rec(p + 1, t));
}
int main() {
  ios::sync_with_stdio(false);
  memset(hoise, -1, sizeof(hoise));
  long long i, j, m, p = 0, a, b, c = 0, d;
  cin >> n;
  for (int i = 0; i <= 2; i++) cin >> in[i];
  for (int i = 0; i <= n - 1; i++) cin >> ar[i];
  cout << rec(0, 0) << '\n';
  return 0;
}
