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
saurabhrathi12:
20170523 20:28:59
Input format mentioned wrong in the question (no of test cases not given). It is correct in example. 

cj23897:
20170514 10:42:19
For those who are stuck.. Just do it on pen and paper and you'll get that 

blame:
20170413 23:44:47
For the input


sultania23:
20170321 13:36:58
mcm. silly mistake caused me 4 wrong ans.. 

jeelapamy:
20170316 18:14:39
@popat ur test cases are wrong 

mrm_196:
20170314 20:32:43
@roopansh I got Accepted using them. 

vineetpratik:
20170305 17:35:03
@popat 120675 is correct answer for your test case


nilabja16180:
20170227 18:54:03
DP with recursion, AC in ONE GO! Last edit: 20170227 18:54:25 

vikas124:
20170227 13:36:13
Last edit: 20170227 13:40:18 

vladimira:
20170226 12:24:27
Good dp problem. AC in one go!

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 