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B. Marvolo Gaunt's Ring

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputProfessor 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* ( - 10^{9} ≤ *p*, *q*, *r* ≤ 10^{9}, 1 ≤ *n* ≤ 10^{5}).

Next line of input contains *n* space separated integers *a* _{1}, *a* _{2}, ... *a* _{ n} ( - 10^{9} ≤ *a* _{ i} ≤ 10^{9}).

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.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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