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

nondescript:
20131024 00:43:05
beautiful DP. thanks! 

Avaneesh Rastogi:
20131018 22:42:43
The answer for 2+1*0*1+1 is >>


samuel:
20130710 02:49:41
Nice DP!! 

technophyle:
20130531 00:31:13
Hint: find analogue...:) 

Aradhya:
20130526 06:42:41
why time limit is set 32 sec o.O ? 1 sec is more than enough.. i used cin cout strings.. etc still 0.63 

Haijun Deng:
20130525 09:50:50
Still Got WA with following cases:


anuj kumar jain:
20130414 01:43:21
recursive solution costed me many TLEs.... but same logic when implemented by looping got accepted....:))) 

Santiago Palacio:
20130107 03:25:20
Time limit is WAY too large. 

Shubham:
20121218 20:24:48
if there were no 0, would greedy solution work? 
Added by:  Simon 
Date:  20050517 
Time limit:  32s 
Source limit:  8082B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL GOSU JSRHINO 
Resource:  Ulm Algorithm Course SoSe 2005 