Inverse Matrix

$P = 998244353$ is a prime. Given an $N \times N$ integer matrix $A$, write a program that computes the inverse of $A$ modulo $P$.

A matrix $B$ with $AB \equiv BA \equiv I_N \pmod P$ is called the inverse of $A$ and is written $A^{-1}$. Two matrices are congruent when the entries in every matching position are congruent modulo $P$. $I_N$ is the $N \times N$ identity matrix, where $I_{i,j} = 0$ for $i \ne j$ and $I_{i,i} = 1$.

$P$ is prime, so the inverse is unique whenever it exists. It exists exactly when the determinant of $A$ is not a multiple of $P$. A matrix whose determinant over the integers is nonzero still has no inverse modulo $P$ if that determinant is divisible by $P$.

The first line contains the size $N$ of the matrix. ($1 \le N \le 500$)

Each of the next $N$ lines describes one row of $A$ and contains $N$ integers. The absolute value of each integer is at most 1,000. A negative entry is read as its residue modulo $P$.

If the inverse of $A$ modulo $P$ exists, print $A^{-1}$ over $N$ lines. Each line holds $N$ integers separated by a single space, and every integer is at least $0$ and less than $P$.

If the inverse does not exist, print no inverse.