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
saurabhrathi12: 2017-05-23 20:28:59

Input format mentioned wrong in the question (no of test cases not given). It is correct in example.

cj23897: 2017-05-14 10:42:19

For those who are stuck.. Just do it on pen and paper and you'll get that

blame: 2017-04-13 23:44:47

For the input
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

I get 120175, not 120675. My solution got accepted, so probably the test cases are not extensive enough.

sultania23: 2017-03-21 13:36:58

mcm. silly mistake caused me 4 wrong ans..

jeelapamy: 2017-03-16 18:14:39

@popat ur test cases are wrong

mrm_196: 2017-03-14 20:32:43

@roopansh I got Accepted using them.

vineetpratik: 2017-03-05 17:35:03

@popat 120675 is correct answer for your test case
Hint: slightly modified MCM

nilabja16180: 2017-02-27 18:54:03

DP with recursion, AC in ONE GO!

Last edit: 2017-02-27 18:54:25
vikas124: 2017-02-27 13:36:13

Last edit: 2017-02-27 13:40:18
vladimira: 2017-02-26 12:24:27

Good dp problem. AC in one go!
MCM was helpfull but took a time becouse those a+b%100 and a*b are confusing a little. Try to solve problem not paying attention to functions a+b and a*b, imagine its some f(a,b) and g(a,b). And you'll have to construct two matrices - one for keeping intermidate results of f(x,y) and second for g(x,y)

To popat => Yes, its right answer

Last edit: 2017-02-26 12:26:18

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