LISA  Pocket Money
Young people spend a lot of money on things like sweets, music CDs, mobile phones and so on. But most young girls/boys have one problem: Their pocket money is not enough for all these jolly things. Little Lisa Listig is one of these poor girls with a small pocket money budget. Last month her pocket money lasted only one week. So she decided to enter into negotiations with her father. Her father Tomm  a mathematician  had an incredibly ingenious idea: He wrote down some fancy digits with operators (+,*) in between them on a sheet of paper and allowed Lisa to insert brackets. Then he declared that the result of that arithmetic expression is Lisa's new pocket money. Now it's Lisa's task to maximize her pocket money. As her father was surprised what a huge sum of money Lisa got for her result, he decided to minimize the result of the expression for his son Manfred. Now it's your task to calculate the results obtained by Lisa and her father.
Input
The first line of input contains the number of testcases k ( k< 5000 ). Each of the following k lines consists of an arithemtic expression. This expression consists of numbers (09) seperated by one of the two operators '*' and '+'. There are no spaces between the characters. Each line contains less than 100 characters.
Output
For each expression output the result obtained by Lisa and the result obtained by her father separated by one space. The results of the calculations are smaller than 2^{64}.
Example
Input: 1 1+2*3+4*5 Output: 105 27
Two possible expressions for the first testcase:
105 = (1+2)*(3+4)*5 27 = 1+2*3+4*5
Added by:  Simon Gog 
Date:  20050517 
Time limit:  32s 
Source limit:  8082B 
Memory limit:  1536MB 
Cluster:  Cube (Intel Pentium G860 3GHz) 
Languages:  All except: ERL JS SCM chicken 
Resource:  Ulm Algorithm Course SoSe 2005 
hide comments
Aadil Ahmad:
20150409 04:55:31
Classic :)


shuks:
20150120 18:19:36
Nice variation of Matrix Chain Multiplication ;) 

Anmol Pandey:
20150119 18:57:36
Nice Classical DP <3


Rajat (1307086):
20141010 02:49:13
!!!!!!!SPOILER ALERT!!!!!!!


Apoorv Gupta:
20140614 17:54:52
What should be the answer for >


Amey Telawane:
20140201 09:45:09
why time limit=32 seconds.? mine was done in 0.21 without using fast io.. 

nitesh kumar:
20140110 14:19:05
classical dp problem but presented differntly.. 

Dewan Mahmud Raihan:
20131229 08:05:23
Nice 2 state dp problem. :) 

Vladimir Torpski:
20131225 12:18:33
This is a bit awful... I have a n^3 solution and got AC in 0.76 seconds? Last edit: 20131225 12:18:52 

Arpit Agarwal:
20131207 22:08:20
Iterative > Recursive with memo 