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
hardik98: 2019-01-18 10:02:30

problem could have been really complicated if there were cases where the value of (a+b)%100 was also important parameter along with min. a*b

little_finger: 2019-01-13 12:53:38

for input in cpp
use while (cin >> n)

whyamievenhere: 2018-12-21 18:17:22

Input needs to be structured nicely.. otherwise nice question.

anshumanc007: 2018-12-18 11:46:57

no. of test case is not given in the problem
c++ users
use while(scanf("%d",&n)==1)

gaurav_2000: 2018-11-08 09:42:28

AC in 1 go!

sachinspoj: 2018-11-04 13:51:56

AC in one go :)
Easy Peasy!!

jmr99: 2018-09-27 21:33:53

****spoiler !!****
matrix chain multiplication.

supriyanta: 2018-08-23 23:26:19

before thinking learn matrix chain multiplication

ayushgupta1997: 2018-08-15 08:55:24

Awesome Problem :) That's why I love spoj :p

masterchef2209: 2018-08-10 08:02:44

good question, learning about MCM would be a great help.
(spoiler-read only if you are stuck even after trying for a long time)



use a array of pairs
for a subproblem from [i,j] try to find min(smoke[i,k]+smoke[k+1,j]+smoke_generated after mixing these two) over all i<=k<j. store it in dp[i][j].second. store new chemical in dp[i][j].first corresponding to min smoke.
print dp[0][n-1].second


Added by:Tomek Czajka
Date:2005-05-03
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