P8053 [COCI 2015/2016 #4] DEATHSTAR

After overcoming many difficulties, you have infiltrated the Death Star. To destroy it, you need an array $a$ of length $n$ to start the Death Star’s self-destruction command. Although you do not know what this array is, your old friend Darth Vader gave you an $n \times n$ matrix $b$ in advance. In this matrix, the element in row $i$ and column $j$ satisfies $b_{i,j}=a_i\operatorname{~and~} a_j$, where $\operatorname{and}$ means the bitwise AND operation. Just when you thought you could directly obtain the array $a$ from this matrix, you found that all elements on the main diagonal were destroyed by a lightsaber. You cannot read their values, so they are temporarily replaced with $0$. Now, based on the other undamaged elements, find **any** array $a$ that satisfies the requirements.

The first line contains an integer $n$, the order of the matrix $b$. Then follow $n$ lines, each containing $n$ integers describing the matrix $b$.

Output one line with $n$ integers, representing an array $a$ that satisfies the conditions. Each element of the array must be a **non-negative integer** not exceeding $10^9$. The testdata guarantees that a solution **exists**, but it is **not guaranteed to be unique**.

**[Sample 1 Explanation]** It is easy to see that one valid array is $a=[1,1,1]$, but please note that this is not the only possible answer. **[Constraints]** For all testdata, $1\leqslant n\leqslant 1000$, $0\leqslant b_{i,j}\leqslant 10^9$. **This problem uses Special Judge**. If you have testdata that can hack the [checker written by the problem setter](https://www.luogu.com.cn/paste/fzkkyhqp), or if you have suggestions to improve the checker, feel free to post them in the discussion area below this problem. **[Source]** This problem is from **_[COCI 2015-2016](https://hsin.hr/coci/archive/2015_2016/) [CONTEST 4](https://hsin.hr/coci/archive/2015_2016/contest4_tasks.pdf) T3 DEATHSTAR_**, using the original test configuration, with a full score of $100$ points. Translated and organized by [Eason_AC](https://www.luogu.com.cn/user/112917). Translated by ChatGPT 5