Sum of a Sequence

There is a sequence of positive integers $A = (A_1, A_2, \dots, A_N)$ of length $N$. You are given a table $S$ that collects the sum of every pair of distinct elements of the sequence. That is, $S(i, j) = A_i + A_j$ when $i \neq j$, and $S(i, j) = 0$ when $i = j$.

Given the table $S$, write a program that reconstructs the original sequence $A$.

The first line contains the length of the sequence $N$. ($2 \le N \le 1000$)

Each of the next $N$ lines contains $N$ integers. The $j$-th integer on the $i$-th line is $S(i, j)$, where $S(i, j) = A_i + A_j$ when $i \neq j$ and $S(i, j) = 0$ when $i = j$. Every element of the sequence is a positive integer not greater than $10^5$.

The sequence $A$ corresponding to the given table $S$ is always unique.

Print the elements of the sequence $A$ in order on the first line, separated by spaces.