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
bani_raheja:
20180328 22:14:39
@kmkhan_014 Kaleem Placed! 

ameyanator:
20180222 22:22:44
Awesome problem! It was fun to find the dp. However I couldn't code a clean implementation of the topdown approach. The comments pointed towards MCM. Read it,studied it ACed it :D 

kmkhan_014:
20180212 09:46:49
@blame the range of co


amulyagaur:
20171221 16:30:35
Took some time... but the outcome was joyful !!


atharva_sarage:
20171219 05:52:48
what should be the answer for test case


kmkhan_014:
20171212 21:21:00
Last edit: 20180511 22:47:28 

Muhammad Faishol Amirul Mukminin:
20171001 11:17:44
The first line of the input is not the number of testcases. But you must read until EOF. Last edit: 20171001 11:24:59 

tommy_trash:
20170820 23:37:35
don't use //ios_base::sync_with_stdio(false);//cin.tie(NULL); it will give WA 

heisenberg0820:
20170623 10:27:21
Read Till EOF...costed me 3 WA's :( 

leafbebop:
20170603 15:17:44
for popat's test case ("100\n1 2 ... 100" one), 120175 or 120675 differs because, I suppose, the last mixture of 100. Note that the problem states colour being from 0 to 99, so it is an invalid input. One deal 100 as colour 0 would get 120175 and others would have 120675. It is hard to say which is correct, for the data case is wrong anyway. 
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 