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
mayank:
20141107 12:19:49
For me the problem amounted to (a%c+b%c)%c=(a+b)%c. :) killed a lot of time! 

Gaurav Ahirwar:
20140924 12:32:49
YippE! Finally Did.. Bottomup Approach!:).. was stuck for one and a half day... good one for beginner like me :) 

Kaushik G Kulkarni:
20140829 20:00:34
My 50th on SPOJ. Nice problem to reach half century . 

Pratyush Kumar:
20140815 08:01:17
For all those confused about WA && TLE, cross check your output with SPOJ forum, google it,


Kanav Vats:
20140806 19:02:15
nice one to learn dp... 

Vivek Thakur:
20140726 23:18:56
learn a lot..!!


Sahil Dua:
20140723 08:50:41
Any tricky case except those mentioned in comments? I am getting WA on 1st test case even.. but clearing all cases mentioned here! 

kelaseek:
20140717 05:31:54
while(scanf("%d",&n)!=1)


albus:
20140716 20:19:27
For people who are new to Dynamic Programming please visit http://www.geeksforgeeks.org/dynamicprogrammingset8matrixchainmultiplication/. This link will help you derive solution to this problem 

pouria:
20140713 10:13:51
it's similar to drink water!!! Last edit: 20140713 10:18:41 
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 