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):
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.
65 5 54 6 92 3 100 0 72 3 520 4 5
053035
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 $$$0$$$.