Laura and Operations
Description
Laura is a girl who does not like combinatorics. Nemanja will try to convince her otherwise.
Nemanja wrote some digits on the board. All of them are either $1$, $2$, or $3$. The number of digits $1$ is $a$. The number of digits $2$ is $b$ and the number of digits $3$ is $c$. He told Laura that in one operation she can do the following:
- Select two different digits and erase them from the board. After that, write the digit ($1$, $2$, or $3$) different from both erased digits.
For example, let the digits be $1$, $1$, $1$, $2$, $3$, $3$. She can choose digits $1$ and $3$ and erase them. Then the board will look like this $1$, $1$, $2$, $3$. After that, she has to write another digit $2$, so at the end of the operation, the board will look like $1$, $1$, $2$, $3$, $2$.
Nemanja asked her whether it was possible for only digits of one type to remain written on the board after some operations. If so, which digits can they be?
Laura was unable to solve this problem and asked you for help. As an award for helping her, she will convince Nemanja to give you some points.
题面翻译
劳拉是一个不喜欢组合学的女孩。尼曼嘉会试着说服她。
尼曼嘉在黑板上写了一些数字。所有数字要么是 1 ，要么是 2 ，要么是 3 。数字 1 的个数是 ? 。数字 2 的个数是 ? ，数字 3 的个数是 ? 。他告诉劳拉，在一次运算中，她可以完成以下操作：
选择两个不同的数字，然后把它们从黑板上擦掉。然后，写出与擦除的两个数字不同的数字( 1 、 2 或 3 )。 例如，数字为 1 、 1 、 1 、 2 、 3 、 3 。她可以选择数字 1 和 3 并擦除它们。这样，黑板上就会出现 1 、 1 、 2 、 3 。之后，她必须写下另一个数字 2 ，因此操作结束后，黑板上将显示 1 , 1 , 2 , 3 , 2 。
尼曼嘉问她，在某些运算后，黑板上是否可能只写一种类型的数字。如果可能，那会是哪些数字呢？
劳拉无法解决这个问题，于是向您求助。作为对你帮助她的奖励，她将说服尼曼嘉给你一些分数。
Input
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^5$). The description of the test cases follows.
The first and only line of each test case contains three integers $a$, $b$, $c$ ($1 \le a, b, c \le 100$) — the number of ones, number of twos, and number of threes, respectively.
Output
For each test case, output one line containing $3$ integers.
The first one should be $1$ if it is possible that after some operations only digits $1$ remain on the board, and $0$ otherwise.
Similarly, the second one should be $1$ if it is possible that after some operations only digits $2$ remain on the board, and $0$ otherwise.
Similarly, the third one should be $1$ if it is possible that after some operations only digits $3$ remain on the board, and $0$ otherwise.
3
1 1 1
2 3 2
82 47 59
1 1 1
0 1 0
1 0 0
Note
In the first test case, Laura can remove digits $2$ and $3$ and write digit $1$. After that, the board will have $2$ digits $1$. She can make it have only digits $2$ or $3$ left by performing a similar operation.
In the second test case, she can remove digits $1$ and $3$ and write a digit $2$. After performing that operation $2$ times, the board will have only digits $2$ left. It can be proven that there is no way to have only digits $1$ or only digits $3$ left.
In the third test case, there is a sequence of operations that leaves only digits $1$ on the board. It can be proven that there is no way to have only digits $2$ or only digits $3$ left.
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