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Vanya and Students 3rd time around

Easy, math


Vanya is extremely curious about the characteristics of her students. She has for each student of her class $$3$$ pieces of information, i.e. their Name, ID and Height. Today, she has decided to play another game with her class. So, the rules of the game are :

This game consists of many turns. In each turn Vanya randomly picks any $$2$$ students of her class. She then notes down on a piece of paper she has, the product of the heights of the $$2$$ students.

She considers each pair of students only and exactly once. That is if Vanya has already written on the piece of paper the product of heights of $$2$$ students $$(i,j)$$, then she will not write it again.

She continues this procedure until each distinct pair of students has been considered. That is, if there are $$N$$ students studying in Vanya's class, then all valid pairs $$(i,j)$$ shall be :

$$ \forall_{i=1}^{N-1} \forall_{j=i+1}^{N} (i,j)$$

Two Pairs $$(i,j)$$ and $$(k,l)$$ are considered to be distinct if $$(i \ne k)$$ or $$(i \ne l)$$ or $$(j \ne k)$$ or $$(j \ne l)$$.

Now, she wonders what is the sum of all the numbers written on this paper. Can you help her out ?

Input Format:

Table : Students

Field Type
Name text
ID text
Height int


Name ID Height
Micro 12abcd 2
Vasya 13abcd 3
Rhezo 14abcd 4




The number of students shall not exceed 20.

The height of each student shall lie between $$1$$ and $$10$$ inclusive.

The length of Name and ID of each student shall lie between $$1$$ and $$20$$ inclusive.


For the sample,

The unique pairs of students are :

1.>(Micro, Vasya). Product=$$(2 \times 3)$$ = $$6$$.

2 .> (Micro, Rhezo). Product= $$(2 \times 4)$$ = $$8$$.

2 ,> (Vasya, Rhezo) . Product = $$(3 \times 4)$$ = $$12$$.

Thus, the answer = $$6+8+12$$=$$26$$.

Time Limit: 5 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: MySQL, PostgreSQL, MSSQL, Oracle Database


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