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
Amit:
20140620 09:19:06
converted to long long int and got AC, How can answer exceed 10^6? 

tyler_durden:
20140616 15:12:05
How long should we carry on taking the input??


viraj:
20140613 06:46:02
can anyone explain how we can solve this problem via dp ? Thanks. 

Kartik:
20140608 20:00:38
How many times do we have to take input ? Number of cases are not defined in the problem. Last edit: 20140608 20:01:16 

Vikas Yadav:
20140606 10:47:49
basic DP!!! Good one to start learning dp!!! Last edit: 20140607 14:58:09 

Guilherme Sena:
20140220 22:18:08
TLE on O(n³)? :( 

IKKA:
20140129 05:30:09
print 0 for n=1 

Tigran Galstyan:
20140101 19:06:10
@neeraj bhat


Vipul Pandey:
20131222 14:54:35
good one to learn dp.. 

Avaneesh Rastogi:
20131025 19:20:35
Last edit: 20140116 16:01:17 
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 