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
Aman Agarwal:
20160625 14:28:38
matrix chain multiplication ✌ Last edit: 20160625 14:29:12 

TP:
20160623 10:44:04
Must check for n=1 , it costs me a WA. Simple Dp :) 

try2catch:
20160120 10:38:45
Spoiler Alert!  "Solution"


abhishekrahul:
20160116 08:13:24
getting tle, why??


saketj:
20151222 11:16:04
[code removed]


rajesh1995:
20151218 13:21:09
can we pick any two consecutive mixtures?


n_bukuri:
20151216 12:43:59
Finally AC :) trying to solve for 2 days...output should be 0 for N=1 

irbis9:
20151120 21:09:16
My second dp on my own, confidence level is increasing. 

sbansalcs:
20151113 09:51:42
Last edit: 20151113 09:51:55 

Jian Luo:
20151018 03:23:54
my first DP, it took me 1 week to do it correctly. But it worth the time. :) 
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 