PROBLEM STATEMENT
You are given a sequence of digits.  You must insert either a '+' (addition) operator or a '*' (multiplication) operator between each pair of adjacent digits in such a way that minimizes the value of the resulting expression.  The expression should be evaluated using the standard order of operations (multiplication has a higher precedence than addition).

You will be given a string sequence.  Perform the procedure described above on the sequence and return the resulting expression.  If there are several possible answers, return the one that comes first lexicographically.  Note that '*' comes before '+' lexicographically.


DEFINITION
Class:OperationsArrangement
Method:arrange
Parameters:string
Returns:string
Method signature:string arrange(string sequence)


CONSTRAINTS
-sequence will contain between 2 and 50 characters, inclusive.
-Each character in sequence will be a digit ('0'-'9').


EXAMPLES

0)
"222"

Returns: "2*2+2"

The minimal result can be obtained in three ways: "2*2+2", "2+2*2" and "2+2+2". The first one comes first lexicographically.

1)
"322"

Returns: "3+2*2"

2)
"307"

Returns: "3*0*7"

3)
"391118571"

Returns: "3+9*1*1*1+8+5+7*1"

4)
"111221911212"

Returns: "1*1*1*2*2*1+9*1*1+2*1*2"