Death Star

Ivan, a young Jedi, has been sent to infiltrate the Death Star and destroy it. Destroying it takes a sequence of $N$ non-negative integers $a_1, a_2, \dots, a_N$, and Ivan does not have that sequence. What he has is a note from his old friend Darth Vader, and the note states the condition the sequence must satisfy.

The note holds a square matrix of size $N$. The value $m_{ij}$ in row $i$ and column $j$ is the bitwise and of $a_i$ and $a_j$. A lightsaber damaged the note, so the main diagonal is unreadable, and the input gives it as 0.

Several sequences can satisfy the condition, and at least one always exists. Recover the one that comes first in lexicographic order.

The first line has the size of the matrix $N$ ($1 \le N \le 1000$).

Each of the next $N$ lines has one row of the matrix: $N$ integers $m_{ij}$ ($0 \le m_{ij} \le 10^9$) separated by single spaces. Every diagonal value $m_{ii}$ is 0, and $m_{ij} = m_{ji}$ holds whenever $i \ne j$. At least one valid sequence exists, and every element of it is at most $10^9$.

Print on one line the lexicographically smallest sequence that satisfies the condition, as $N$ integers separated by single spaces.

Lexicographic comparison reads two sequences from the first element and takes the one with the smaller value at the first position where they differ.