A1502.[COCI-2012_2013-contest6]#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 ≤ N ≤ 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 ≠ 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 spaceseparated positive integers).