Synthetic Kadomatsu

You have N bamboos. The lengths (in centimeters) of these are l_1, l_2, ..., l_N, respectively.

Your objective is to use some of these bamboos (possibly all) to obtain three bamboos of length A, B, C. For that, you can use the following three kinds of magics any number:

• Extension Magic: Consumes 1 MP (magic point). Choose one bamboo and increase its length by 1.
• Shortening Magic: Consumes 1 MP. Choose one bamboo of length at least 2 and decrease its length by 1.
• Composition Magic: Consumes 10 MP. Choose two bamboos and combine them into one bamboo. The length of this new bamboo is equal to the sum of the lengths of the two bamboos combined. (Afterwards, further magics can be used on this bamboo.)

At least how much MP is needed to achieve the objective?

Constraints

• 3 \leq N \leq 8
• 1 \leq C < B < A \leq 1000
• 1 \leq l_i \leq 1000
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N A B C l_1 l_2 : l_N

Output

Print the minimum amount of MP needed to achieve the objective.

Examples

Input

5 100 90 80 98 40 30 21 80

Output

23

Input

8 100 90 80 100 100 90 90 90 80 80 80

Output

0

Input

8 1000 800 100 300 333 400 444 500 555 600 666

Output

243

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A B C l_1 l_2 : l_N

outputFormat

Output

Print the minimum amount of MP needed to achieve the objective.

Examples

Input

5 100 90 80 98 40 30 21 80

Output

23

Input

8 100 90 80 100 100 90 90 90 80 80 80

Output

0

Input

8 1000 800 100 300 333 400 444 500 555 600 666

Output

243

样例

8 1000 800 100
300
333
400
444
500
555
600
666

243