Be Together

AtCoder

IDarc059_a

Time2000ms

Memory256MB

Difficulty—

Evi has $N$ integers $a_1,a_2,..,a_N$. His objective is to have $N$ equal **integers** by transforming some of them. He may transform each integer at most once. Transforming an integer $x$ into another integer $y$ costs him $(x-y)^2$ dollars. Even if $a_i=a_j (i≠j)$, he has to pay the cost separately for transforming each of them (See Sample 2). Find the minimum total cost to achieve his objective. ## Constraints * $1≦N≦100$ * $-100≦a_i≦100$ ## Input The input is given from Standard Input in the following format: $N$ $a_1$ $a_2$ ... $a_N$ [samples]

Samples

Input #1

2
4 8

Output #1

8

Transforming the both into $6$s will cost $(4-6)^2+(8-6)^2=8$ dollars, which is the minimum.

Input #2

3
1 1 3

Output #2

3

Transforming the all into $2$s will cost $(1-2)^2+(1-2)^2+(3-2)^2=3$ dollars. Note that Evi has to pay $(1-2)^2$ dollar separately for transforming each of the two $1$s.

Input #3

3
4 2 5

Output #3

5

Leaving the $4$ as it is and transforming the $2$ and the $5$ into $4$s will achieve the total cost of $(2-4)^2+(5-4)^2=5$ dollars, which is the minimum.

Input #4

4
-100 -100 -100 -100

Output #4

0

Without transforming anything, Evi's objective is already achieved. Thus, the necessary cost is $0$.

API Response (JSON)

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    "name": "Be Together",
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      "content": "Evi has $N$ integers $a_1,a_2,..,a_N$. His objective is to have $N$ equal **integers** by transforming some of them. He may transform each integer at most once. Transforming an integer $x$ into anothe",
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    "difficulty": "None",
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      "statement_type": "Markdown",
      "content": "Evi has $N$ integers $a_1,a_2,..,a_N$. His objective is to have $N$ equal **integers** by transforming some of them.\nHe may transform each integer at most once. Transforming an integer $x$ into anothe...",
      "is_translate": false,
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