CF2256A Three Numbers on the Blackboard

Rain is falling outside the Fairy Warehouse, so Chtholly, Nephren, and Ithea spend the afternoon playing a game in the common room. Ithea writes three non-negative integers $ a $ , $ b $ , and $ c $ on the blackboard. Chtholly may perform the following operation an arbitrary number of times (possibly zero): - Choose one of the three current integers and replace it with the sum of the other two current integers. The other two integers remain unchanged. For example, starting from $ (3,5,11) $ , she can replace $ 11 $ with $ 3+5 $ , obtaining $ (3,5,8) $ . Nephren wants to know the minimum range $ ^{\text{∗}} $ of the three integers that Chtholly can obtain. Help her find it! $ ^{\text{∗}} $ The range of a non-empty finite collection of numbers is defined as its maximum value minus its minimum value. In particular, the range of three numbers $ x $ , $ y $ , and $ z $ is $ \max(x,y,z)-\min(x,y,z) $ .

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 100 $ ). The description of the test cases follows. The only line of each test case contains three integers $ a $ , $ b $ , and $ c $ ( $ 0 \le a,b,c \le 10^9 $ ) — the integers initially written on the blackboard.

For each test case, output a single integer — the minimum possible range of the three integers.

In the first test case, all three integers are already equal, so their range is $ 0 $ . In the second test case, performing no operation gives the range $ 9-4=5 $ . It can be shown that no sequence of operations can produce a smaller range. In the third test case, Chtholly can replace $ 10 $ with $ 2+3=5 $ . The three integers become $ (2,3,5) $ , whose range is $ 5-2=3 $ . In the fourth test case, Chtholly can replace $ 7 $ with $ 0+0=0 $ . All three integers then become $ 0 $ .