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## ONP - Transform the Expression |

Transform the algebraic expression with brackets into RPN form (Reverse Polish Notation). Two-argument operators: +, -, *, /, ^ (priority from the lowest to the highest), brackets ( ). Operands: only letters: a,b,...,z. Assume that there is only one RPN form (no expressions like a*b*c).

### Input

t[the number of expressions <=100]expression[length <=400] [other expressions]

Text grouped in [ ] does not appear in the input file.

### Output

Theexpressions in RPN form, one per line.

### Example

Input: 3 (a+(b*c)) ((a+b)*(z+x)) ((a+t)*((b+(a+c))^(c+d))) Output: abc*+ ab+zx+* at+bac++cd+^*

Added by: | mima |

Date: | 2004-05-01 |

Time limit: | 5s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | C++ 4.3.2 CPP14 |

Resource: | - |