Bob and three of his friends, James, Mark, and John, are standing in a row at the entrance of a cave to explore special equations (they stand in order as mentioned).

The cave contains $n$ roomes and the $i_{th}$ room contains an integer number $a_i$.

John did not see any special equations before. So, Bob will show some special equations to John.

Initially, Bob has four numbers $w$, $x$, $y$, and $z$. He will take the first number, James will take the second number, Mark will take the third number, and John will take the last number.

They will enter the cave and everyone will take a number from any room. No one can take Bob's number until everyone in front of him takes his number and they cannot go back again.

After they leave the cave, everyone will multiply his initial number with the number he chose in the cave then the special equation will be computed.

Suppose that the final numbers after multiplying will be $w_1$, $x_1$, $y_1$, and $z_1$, then the magical equation will be: 

$x_1$ - $w_1$ + $z_1$ - $y_1$

Help Bob to know what is the maximum answer he can get from the special equation.

Formally, you are required to select 4 indices $1 \le i_1 < i_2 < i_3 < i_4 \le n$ to maximize $-a_{i_1} \times w + a_{i_2} \times x - a_{i_3} \times y + a_{i_4} \times z$.

Input format

• The first line contains one integer $n$ denoting the number of rooms 
• The second line contains $n$ space-separated integers.
• The last line contains four integers $w$, $x$, $y$, and $z$.

Output format

Print the maximum answer that Bob can get from the special equation.

Constraints

$4 \le   n  \le  10^5$

$1 \le  a_i  \le {10^6}$

$1 \le w, x, y, z  \le  {10^9}$