1947. Sum

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.

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).

2
0 2
2 0

1 1

4
0 3 6 7
3 0 5 6
6 5 0 9
7 6 9 0

2 1 4 5