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() {
  iostream::sync_with_stdio(false);
  cin.tie(NULL);
  long long n;
  cin >> n;
  vector<long long> b(3);
  vector<long long> a(n);
  cin >> b[0] >> b[1] >> b[2];
  for (long long i = (0); i < (n); ++i) {
    cin >> a[i];
  }
  vector<long long> aa(a.begin(), a.end());
  long long p = b[0], q = b[1], r = b[2];
  vector<long long> lmax(n), rmax(n), lmin(n), rmin(n);
  lmax[0] = a[0];
  lmin[0] = a[0];
  rmax[n - 1] = a[n - 1];
  rmin[n - 1] = a[n - 1];
  sort(b.begin(), b.end());
  sort(aa.begin(), aa.end());
  for (long long i = (1); i < (n); ++i) {
    if (a[i] > lmax[i - 1])
      lmax[i] = a[i];
    else
      lmax[i] = lmax[i - 1];
    if (a[i] < lmin[i - 1])
      lmin[i] = a[i];
    else
      lmin[i] = lmin[i - 1];
  }
  for (int i = n - 2; i >= 0; i--) {
    if (a[i] > rmax[i + 1])
      rmax[i] = a[i];
    else
      rmax[i] = rmax[i + 1];
    if (a[i] < rmin[i + 1])
      rmin[i] = a[i];
    else
      rmin[i] = rmin[i + 1];
  }
  if (b[0] >= 0) {
    cout << aa[n - 1] * (b[0] + b[1] + b[2]);
    exit(0);
  }
  if (b[2] <= 0) {
    cout << aa[0] * (b[0] + b[1] + b[2]);
    exit(0);
  }
  long long sm = LONG_LONG_MIN;
  if (q >= 0 && r >= 0) {
    for (int i = n - 1; i >= 0; i--) {
      if (rmax[i] * (q + r) + lmin[i] * p > sm)
        sm = rmax[i] * (q + r) + lmin[i] * p;
    }
  } else if (p >= 0 && q >= 0) {
    for (int i = n - 1; i >= 0; i--) {
      if ((q + p) * lmax[i] + rmin[i] * r > sm)
        sm = lmax[i] * (q + p) + rmin[i] * r;
    }
  } else if (p >= 0 && r >= 0) {
    for (int i = 0; i < n; i++) {
      if (lmax[i] * p + rmax[i] * r + a[i] * q > sm)
        sm = lmax[i] * p + rmax[i] * r + a[i] * q;
    }
  } else if (p >= 0) {
    for (int i = 0; i < n; i++) {
      if (lmax[i] * p + rmin[i] * (r + q) > sm)
        sm = lmax[i] * p + rmin[i] * (r + q);
    }
  } else if (q >= 0) {
    for (int i = 0; i < n; i++) {
      if (lmin[i] * p + rmin[i] * (r) + q * a[i] > sm)
        sm = lmin[i] * p + rmin[i] * (r) + q * a[i];
    }
  } else if (r >= 0) {
    for (int i = 0; i < n; i++) {
      if (lmin[i] * (p + q) + rmax[i] * (r) > sm)
        sm = lmin[i] * (p + q) + rmax[i] * (r);
    }
  }
  cout << sm;
}
