NWERC 2017 Open Contest

#### Start

2017-11-26 11:30 CET

## NWERC 2017 Open Contest

#### End

2017-11-26 16:30 CET
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# Problem HHigh Score

The Great Pyramid of Giza; one of the seven wonders. By Nina-no, licensed under CC BY-SA 3.0
Mårten and Simon enjoy playing the popular board game Seven Wonders, and have just finished a match. It is now time to tally the scores.

One of the ways to score in Seven Wonders is through the use of Science. During the game, the players may collect a number of Science tokens of three different types: Cog, Tablet, and Compass. If a player has $a$ Cogs, $b$ Tablets and $c$ Compasses, that player gets $a^2 + b^2 + c^2 + 7 \cdot \min (a, b, c)$ points.

However, the scoring is complicated by the concept of Wildcard Science tokens. For each Wildcard Science token a player has, she may count that as one of the three ordinary types of Science tokens. For instance, the first player in Sample Input 1 has $2$ Cogs, $1$ Tablet, $2$ Compasses, and $1$ Wildcard Science, so could thus choose to have the distributions $(3, 1, 2), (2, 2, 2)$ or $(2, 1, 3)$ of Cogs, Tablets and Compasses, respectively. The possible scores for this player are then $3^2 + 1^2 + 2^2 + 7 \cdot 1 = 21$, $2^2 + 2^2 + 2^2 + 7 \cdot 2 = 26$ and $2^2 + 1^2 + 3^2 + 7 \cdot 1 = 21$ depending on how the Wildcard Science is assigned. Thus, the maximum score for this player is $26$.

Given the number of tokens each player in the game has, compute the maximum possible score that each of them can achieve if they assign their Wildcard Science tokens optimally.

## Input

The input consists of:

• One line with an integer $n$ ($3 \le n \le 7$), the number of players in the game.

• $n$ lines, each with four integers $a$, $b$, $c$, $d$ ($0 \le a, b, c, d \le 10^9$), giving the number of Cog, Tablet, Compass, and Wildcard Science tokens of a player.

## Output

For each player, in the same order they are given in the input, output the maximum score the player may get.

Sample Input 1 Sample Output 1
3
2 1 2 1
3 2 1 0
1 3 0 1

26
21
18