#### Registered Users Only

Please login to view and utilize this feature.

Alice got lost in the Wonderland shopping mall! The mall was so big, and she totally had no sense of direction. Luckily, she found a shopping directory! To locate the store that she was looking for, she had to key in the unit number of that store, N, into the searching bar.(N is an integer, 0 < **N** ≤ 20000) But the problem was that she was in Wonderland so everything must only be written in digits 0 and 2 with brackets. Although Alice did not have any sense of direction, she was very good at math! She found that every positive integer can be represented by he sum of the powers of 2. For example, 137 = 128+8+1 = 2^7+2^3+2^0. But clearly it was not enough because she still had 7, which was forbidden in the Wonderland. So she reduced it further: 7 = 2^2+2+2^0(note that 2^1 is represented by 2). Similarly, 3 = 2+2^0. In this way, she obtained an expression which only contained 2 and 0: 137 = 128+8+1 = 2^(2^2+2+2^0)+2^(2+2^0)+2^0. Since the symbol^ was also forbidden in the Wonderland, Alice had to represent a^b as a(b). So the final expression she should key in would be: 137 = 2(2(2)+2+2(0))+2(2+2(0))+2(0). She was too lazy to think so she called you up and asked you to write a program for her to output the "02" expression of the unit number of the store.

### Input

Each input contains only one line, which contains the unit number of the store, **N**, 0 < **N** ≤ 20000.

### Output

Each output contains only one line, which is the "02" expression of **N**.

Your output should contains only digits 0 and 2 and brackets.

### Limits

Subtask 1 (11%): 0 < **N** ≤ 100

Subtask 2 (23%): 100 < **N** ≤ 5000

Subtask 3 (66%): 1000 < **N** ≤ 20000

Subtask 4 (0%): Sample testcases

### Sample Input

137

### Sample Output

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

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 11 | 5 | 1s | 32MB | Minimum |

2 | 23 | 4 | 1s | 32MB | Minimum |

3 | 66 | 5 | 1s | 32MB | Minimum |

4 | 0 | 1 | 1s | 32MB | Minimum |

### Judge Compile Command

g++ ans.cpp -o wonderland -Wall -static -O2 -lm -m64 -s -w -std=gnu++14 -fmax-errors=512