Automatic Sprayer 2

A farm is divided into $n \times n$ unit squares with $n$ rows and $n$ columns. Let $(i, j)$ denote the unit square in the $i$-th row and the $j$-th column ($1 \le i \le n$, $1 \le j \le n$).

The distance between two squares $(i_1, j_1)$ and $(i_2, j_2)$ is the Manhattan distance $d\left(\left(i_1, j_1\right), \left(i_2, j_2\right)\right) = |i_1 - i_2| + |j_1 - j_2|$.

The farm has automatic sprayers that spray fertilizer solution or herbicide so the owner can produce grain efficiently.

Each sprayer lies entirely in a unit square. The sprayer in $(x,y)$ sprays $A_{x,y}$ liters of solution onto every unit square. $A_{x,y}$ is a nonnegative integer.

For the sprayer in $(x, y)$ to spray solution onto $(i, j)$, the energy required is exactly $d((x, y), (i, j)) \times A_{x,y}$. For each square $(i, j)$, let $E_{i,j}$ be the sum of energies needed for all sprayers to spray the square $(i, j)$.

Given the matrix $E$, write a program that outputs any matrix $A$ that corresponds to $E$. $E$ is given so that such a matrix $A$ of nonnegative integers whose sum is at most $10^{12}$ exists.

The first line contains a single positive integer $n$ ($2 \le n \le 1\,000$).

The next $n$ lines each contain $n$ integers. The $j$-th ($1 \le j \le n$) integer in the $i$-th ($1 \le i \le n$) line is $E_{i,j}$ ($0 \le E_{i,j} \le 10^{16}$).

The input is given so that a matrix $A$ consisting of only nonnegative integers whose sum is at most $10^{12}$ exists and can produce $E$.

Output $n$ lines, each containing $n$ integers. The $y$-th ($1 \le y \le n$) integer in the $x$-th ($1 \le x \le n$) line is $A_{x,y}$.