P13420 [COCI 2012/2013 #6] SUME

Once upon a time, there existed a sequence A consisting of $N$ positive integers. You don't know the sequence itself, but you do know the sum of every two elements of the sequence. Find the sequence $A$!

The first line of input contains the positive integer $N$ ($2 \leq N \leq 1000$). Each of the following $N$ lines contains $N$ positive integers smaller than or equal to $100\,000$, forming the table S. The following relations hold: $S(i, j) = A[i] + A[j]$ for $i \neq j$, and $S(i, j) = 0$ for $i = j$. Here $S(i, j)$ denotes the number in the $i^{th}$ row and $j^{th}$ column of the table, and $A[i]$ denotes the $i^{th}$ element of the sequence A. It is guaranteed that for any input data set there exists a unique sequence of positive integers A with the given properties.

The first and only line of output must contain the required sequence A (in the form of $N$ space-separated positive integers).