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Make a Number Expression

Few years ago, an esoteric programming language named 아희(Aheui) was created. Well, actually you don't need to know about this language or Korean characters.

Aheui uses stacks and a queue, but this time we use one stack and ignore other stacks and queue. You can push a number between 2 and 9 into a stack. You can do arithmetic operations by popping two numbers and pushing result. And you can duplicate a top number.

So, when I need a big number in Aheui, making a number was not an easy work. Push, push, multiply, duplicate, push, multiply, push, add…. It takes too much time and sometimes waste of bytes. I need a shortest expressions.

Summary

Your task is to write a function or a program which takes a number n (0 <= n <= 1000000) and returns concatenation of tokens.

Tokens are basically a postfix notation. Tokens are consisted of

• Number between 2 and 9, which means "push number into stack"
• +, -, /, *, which means "pop two numbers from stack, do arithmetic operation, push the result into stack". All calculations are in integer.
• >, which means "duplicate a top number"

Tokens will be concatenated with empty string, so 5 5 + will be 55+.

After calculations, n must be on the top of the stack.

Sample input and output

INPUT = 0
OUTPUT = 22-
(or 33-, 44-, whatever)

INPUT = 1
OUTPUT = 22/
(or 32-, 33/, whatever)

INPUT = 5
OUTPUT = 5
(We don't need calculations, just push)

INPUT = 64
OUTPUT = 88*
(or 8>*)

INPUT = 1337
OUTPUT = 75*2+>*48*-
(This may not be a shortest solution)


Scoring

This is a list of test cases. Test cases are seperated by a new line character. You may write a test script which converts those bunch of numbers to string of tokens, or you can do it by your hand.

Let

• S = size of complete function or program
• O = length of converted strings
• I = size of test cases (In this case, I = 526)

Then your score will be S * (O / I). Sizes are in bytes.

S includes function declarations, #includes, imports, whatever. Test script is not counted.

Scoring example

Let S is 150.

Sample Test cases

0
1
5
64
1337


Sample Output

22-22/588*75*2+>*48*-


In this case, I = 9, and O = 21. So your score is 150 * (21 / 9) = 350.

Rules

• Standard "loopholes" are forbidden.
• Lowest score wins.
• If there is a tie, smaller code size wins.
• Winner will be selected after three weeks (2014-08-04).

I wrote a validator in Node.js. Put input.txt and output.txt in same directory, and run node validator.js.

And I found two-year-old similar question. But scoring is different (this question includes code size in score), and this question can't use 1. So I hope it's not a duplicate.