A.M. Deviation

题意翻译

## 题目描述 给出 3 个数 $a_1,a_2,a_3$，现有一种操作可以在 $a_1,a_2,a_3$ 中任选两个数，使其中一个 +1，另一个 -1。操作次数不限。 要求最小化 $|a_1+a_3-2\times a_2|$。 ## 输入格式 第一行输入一个整数 $t$ 表示数据组数。 每组数据读入一行 3 个整数 $a_1,a_2,a_3$。 ## 输出格式 对于每组数据输出一行一个整数表示最小的 $|a_1+a_3-2\times a_2|$。 ## 数据范围 $1\le t\le 5000,1\le a_1,a_2,a_3\le 10^8$。

题目描述

A number $ a_2 $ is said to be the arithmetic mean of two numbers $ a_1 $ and $ a_3 $ , if the following condition holds: $ a_1 + a_3 = 2\cdot a_2 $ . We define an arithmetic mean deviation of three numbers $ a_1 $ , $ a_2 $ and $ a_3 $ as follows: $ d(a_1, a_2, a_3) = |a_1 + a_3 - 2 \cdot a_2| $ . Arithmetic means a lot to Jeevan. He has three numbers $ a_1 $ , $ a_2 $ and $ a_3 $ and he wants to minimize the arithmetic mean deviation $ d(a_1, a_2, a_3) $ . To do so, he can perform the following operation any number of times (possibly zero): - Choose $ i, j $ from $ \{1, 2, 3\} $ such that $ i \ne j $ and increment $ a_i $ by $ 1 $ and decrement $ a_j $ by $ 1 $ Help Jeevan find out the minimum value of $ d(a_1, a_2, a_3) $ that can be obtained after applying the operation any number of times.

输入输出格式

输入格式

The first line contains a single integer $ t $ $ (1 \le t \le 5000) $ — the number of test cases. The first and only line of each test case contains three integers $ a_1 $ , $ a_2 $ and $ a_3 $ $ (1 \le a_1, a_2, a_3 \le 10^{8}) $ .

输出格式

For each test case, output the minimum value of $ d(a_1, a_2, a_3) $ that can be obtained after applying the operation any number of times.

输入输出样例

输入样例 #1

3
3 4 5
2 2 6
1 6 5

输出样例 #1

0
1
0

说明

Note that after applying a few operations, the values of $ a_1 $ , $ a_2 $ and $ a_3 $ may become negative. In the first test case, $ 4 $ is already the Arithmetic Mean of $ 3 $ and $ 5 $ . $ d(3, 4, 5) = |3 + 5 - 2 \cdot 4| = 0 $ In the second test case, we can apply the following operation: $ (2, 2, 6) $ $ \xrightarrow[\text{increment $ a\_2 $ }]{\text{decrement $ a\_1 $ }} $ $ (1, 3, 6) $ $ d(1, 3, 6) = |1 + 6 - 2 \cdot 3| = 1 $ It can be proven that answer can not be improved any further. In the third test case, we can apply the following operations: $ (1, 6, 5) $ $ \xrightarrow[\text{increment $ a\_3 $ }]{\text{decrement $ a\_2 $ }} $ $ (1, 5, 6) $ $ \xrightarrow[\text{increment $ a\_1 $ }]{\text{decrement $ a\_2 $ }} $ $ (2, 4, 6) $ $ d(2, 4, 6) = |2 + 6 - 2 \cdot 4| = 0 $