MIXTURES  Mixtures
Harry Potter has n mixtures in front of him, arranged in a row. Each mixture has one of 100 different colors (colors have numbers from 0 to 99).
He wants to mix all these mixtures together. At each step, he is going to take two mixtures that stand next to each other and mix them together, and put the resulting mixture in their place.
When mixing two mixtures of colors a and b, the resulting mixture will have the color (a+b) mod 100.
Also, there will be some smoke in the process. The amount of smoke generated when mixing two mixtures of colors a and b is a*b.
Find out what is the minimum amount of smoke that Harry can get when mixing all the mixtures together.
Input
There will be a number of test cases in the input.
The first line of each test case will contain n, the number of mixtures, 1 <= n <= 100.
The second line will contain n integers between 0 and 99  the initial colors of the mixtures.
Output
For each test case, output the minimum amount of smoke.
Example
Input: 2 18 19 3 40 60 20 Output: 342 2400
In the second test case, there are two possibilities:
 first mix 40 and 60 (smoke: 2400), getting 0, then mix 0 and 20 (smoke: 0); total amount of smoke is 2400
 first mix 60 and 20 (smoke: 1200), getting 80, then mix 40 and 80 (smoke: 3200); total amount of smoke is 4400
The first scenario is a much better way to proceed.
hide comments
Piyush Nirmal:
20150731 05:03:41
a nice problem. 

just_code21:
20150729 19:21:40
very good ques for matrix multiplication


rk:
20150711 15:46:01
my bad missed some states as was unknown to matrix chain algo but after that cakewalk :). 

palash ahuja:
20150627 14:20:30
dp solution should work Last edit: 20150627 14:29:51 

:.Mohib.::
20150620 17:12:48
Matrix chain multiplication ;) 

Sluggish_Fool:
20150619 13:42:30
100th on a DP!! :D 

Pagan Min:
20150408 15:06:21
first question on matrix chain multiplication...nice one 

Shubham Bansal:
20150313 15:22:40
a very nice question for starters.. :) 

Sahil Sharma:
20150104 10:47:15
The input file DOES NOT end with a \n and hence if you're following something like :


Anne:
20150104 04:17:04
d/\p Last edit: 20150104 04:18:58 
Added by:  Tomek Czajka 
Date:  20050503 
Time limit:  3s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  Purdue Programming Contest Training 