+ محدودیت زمان: ۱ ثانیه + محدودیت حافظه: ۲۵۶ مگابایت ---------- Ultron, the mischievous alien robot wants to attack the earth with his army and wipe out the humans, but, everything is not going according to his plan as there are a group of superheroes called “The Avengers” who are fighting against the alien army. Ultron knows that the avengers can take down the army and he can’t beat all of them unless he finds a way to trap them all somewhere and kill all of them by exploding the area. He has learned the ability of breaking and lifting a piece of land by meditation from his master but because he was never paying enough attention to his lessons (he was always dreaming about his evil plans!), he is only able to lift a square shaped piece of land. Since this trick takes a lot of energy from him, he prefers to crack the smallest possible square. Now here is the deal, he gives the position and speed of all the avengers at time “0” to you, if you give him the minimum size of square side that contains all of the avengers from now, he will let you and your laptop to happily live forever on the earth.(for simplicity, he wants the sides of squares to be aligned with Coordinate axes).  # ورودی The first line of input shows the number of test cases $T$. Each test case contains an integer $N$ and is followed by $N$ lines. $$1 \leq N \leq 100\,000$$ Each line consists of $4$ floating point numbers $X, Y, V_X, V_Y$ indicating starting position and speed vector of each avengers. $$ -10\,000 \leq X , Y \leq 10\,000$$ $$ -100 \leq V_X, V_Y \leq 100$$ You can assume the maximum time is $10^9$ # خروجی For each test case, print the minimum side of the square which all the avengers could be fitted into. # مثال‌ها ## ورودی نمونه ۱ ``` 3 4 3 12 3 0 9 14 0 0 6 6 2 2 12 9 -3 0 3 0 0 1 1 3.5 0 -1 0 0 -1 -1 -1 3 10 10 -1 -0.5 2 4 1 1 -10 15 4 -1.75 ``` ## خروجی نمونه ۱ ``` 5.00 3.50 0.00 ```

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