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·a i + q·a j + r·a k for given p, q, r and array a 1, a 2, … a n 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 a 1, a 2, … a n ( - 109 ≤ a i ≤ 109).
Output
Output a single integer the maximum value of p·a i + q·a j + r·a k 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.
Solution:
#include <bits/stdc++.h> using namespace std; const int N = 1234567; int a[N]; long long L[N], R[N]; int main() { long long p, q, r; int n; cin >> n >> p >> q >> r; for (int i = 0; i < n; i++) { scanf("%d", a + i); } L[0] = p * a[0]; for (int i = 1; i < n; i++) { L[i] = max(L[i - 1], p * a[i]); } R[n - 1] = r * a[n - 1]; for (int i = n - 2; i >= 0; i--) { R[i] = max(R[i + 1], r * a[i]); } long long ans = (long long) (-9e18); for (int i = 0; i < n; i++) { ans = max(ans, L[i] + q * a[i] + R[i]); } cout << ans << endl; return 0; }