Question 1095: 2 power exercise Recursion

Description:

Every positive number can be presented by the exponential form. For example, 137 = 2 ^ 7 + 2 ^ 3 + 2 ^ 0.

Let's present a ^ B by the Form A (B ). then 137 is presented by 2 (7) + 2 (3) + 2 (0 ). since 7 = 2 ^ 2 + 2 + 2 ^ 0 and 3 = 2 + 2 ^ 0,137 is finally presented by 2 (2 (2) + 2 + 2 (0 )) + 2 (2 + 2 (0) + 2 (0 ).
 
Given a positive number N, your task is to present n with the exponential form which only contains the digits 0 and 2.

Input:

For each case, the input file contains a positive integer n (n <= 20000 ).

Output:

For each case, You shocould output the exponential form of n a single line. Note that, There shocould not be any additional white spaces in the line.

Sample input:

1315

Sample output:

 
2 (2 (2 + 2 (0) + 2) + 2 (2 (2 + 2 (0) + 2 (2 (2) + 2 (0 )) + 2 + 2 (0)
 

 Package Shanghai Jiao Tong University;

 Import Java. util. vendor;

 Public   Class Power: 1095 {
 Static   Int N;
 Public   Static   Void Main (string [] ARGs ){
Scanner S = New Using (system. In );
 While (S. hasnextint ()){
N = S. nextint ();
System. Out. println (f (n ));
}
}
 Static String F ( Int N ){
Stringbuffer sb = New Stringbuffer ();
 If (N <8 ){
 Switch (N ){
Case 0: Return "0 ";
 Case 1: Return "";
 Case 2: Return "2 ";
 Case 3: Return "2 + 2 (0 )";
 Case 4: Return "2 (2 )";
 Case 5: Return "2 (2) + 2 (0 )";
 Case 6: Return "2 (2) + 2 ";
 Case 7: Return "2 (2) + 2 + 2 (0 )";
}
} Else {
String temp = integer. tobinarystring (N );
 Int Len = temp. Length ();
 For ( Int I = 0; I <Len; I ++ ){
 If (Temp. charat (I) = '1 '){
 If (I! = 0)
SB. append ("+ ");
SB. append ("2 (");
SB. append (f (len-i-1 ));
SB. append (")");
}
}
}
 Return SB. tostring (). replaceall ("\\(\\)","");
}
}