#define PROBLEM "https://judge.yosupo.jp/problem/inverse_matrix"
#include "../../cpp/template/template.cpp"
#include "../../cpp/data-structure/mod-int/mod-int.cpp"
#include "../../cpp/math/matrix.cpp"
int main(){
int n;cin>>n;
mat<mint> A(n,n);
cin >> A;
auto z = A.inv();
if(!z.first) cout << -1 << endl;
else cout << z.second << endl;
return 0;
}
#line 1 "cpp/z_test/yosupo-inverse_matrix.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/inverse_matrix"
#line 2 "cpp/template/template.cpp"
//yukicoder@cpp17
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <cctype>
#include <climits>
#include <cassert>
#include <string>
#include <vector>
#include <set>
#include <stack>
#include <queue>
#include <map>
#include <random>
#include <bitset>
#include <complex>
#include <utility>
#include <numeric>
#include <functional>
using namespace std;
using ll = long long;
using P = pair<ll,ll>;
const ll MOD = 998244353;
const ll MODx = 1000000007;
const int INF = (1<<30)-1;
const ll LINF = (1LL<<62LL)-1;
const double EPS = (1e-10);
P ar4[4] = {{0,1},{0,-1},{1,0},{-1,0}};
P ar8[8] = {{-1,-1},{-1,0},{-1,1},{0,-1},{0,1},{1,-1},{1,0},{1,1}};
template <typename T> vector<T> make_vector(size_t a, T b) { return vector<T>(a, b); }
template <typename... Ts> auto make_vector(size_t a, Ts... ts) { return vector<decltype(make_vector(ts...))>(a, make_vector(ts...)); }
/*
確認ポイント
cout << fixed << setprecision(n) << 小数計算//n桁の小数表記になる
計算量は変わらないが楽できるシリーズ
min(max)_element(iter,iter)で一番小さい(大きい)値のポインタが帰ってくる
count(iter,iter,int)でintがiterからiterの間にいくつあったかを取得できる
*/
/* comment outed because can cause bugs
__attribute__((constructor))
void initial() {
cin.tie(0);
ios::sync_with_stdio(false);
}
*/
#line 4 "cpp/z_test/yosupo-inverse_matrix.test.cpp"
#line 2 "cpp/data-structure/mod-int/mod-int.cpp"
template <int mod>
struct ModInt{
int n;
ModInt():n(0){}
ModInt(long long n_):n(n_ >= 0 ? n_%mod : mod - ((-n_)%mod) ){}
ModInt(int n_):n(n_ >= 0 ? n_%mod : mod - ((-n_)%mod) ){}
ModInt &operator+=(const ModInt &p){
if((n+=p.n) >= mod)n-=mod;
return *this;
}
ModInt &operator-=(const ModInt &p){
n+=mod-p.n;
if(n >= mod)n-=mod;
return *this;
}
ModInt &operator*=(const ModInt &p){
n = (int) ((1LL*n*p.n)%mod);
return *this;
}
ModInt &operator/=(const ModInt &p){
*this *= p.inverse();
return *this;
}
ModInt operator-() const {return ModInt(-n);}
ModInt operator+(const ModInt &p) const {return ModInt(*this) += p;}
ModInt operator-(const ModInt &p) const {return ModInt(*this) -= p;}
ModInt operator*(const ModInt &p) const {return ModInt(*this) *= p;}
ModInt operator/(const ModInt &p) const {return ModInt(*this) /= p;}
bool operator==(const ModInt &p) const {return n==p.n;}
bool operator<(const ModInt &p) const {return n<p.n;}
bool operator>(const ModInt &p) const {return n>p.n;}
bool operator>=(const ModInt &p) const {return n>=p.n;}
bool operator<=(const ModInt &p) const {return n<=p.n;}
bool operator!=(const ModInt &p) const {return n!=p.n;}
ModInt inverse() const {
int a = n,b = mod,u = 1,v = 0;
while(b){
int t = a/b;
a -= t*b; swap(a,b);
u -= t*v; swap(u,v);
}
return ModInt(u);
}
ModInt pow(int64_t z) const {
ModInt ret(1),mul(n);
while(z > 0){
if(z & 1) ret *= mul;
mul *= mul;
z >>= 1;
}
return ret;
}
int getMod() const {
return mod;
}
friend ostream &operator<<(ostream &os, const ModInt &p){
return os << p.n;
}
friend istream &operator>>(istream &is, ModInt &a){
int64_t t;
is >> t;
a = ModInt<mod> ((long long)t);
return (is);
}
};
using mint = ModInt<MOD>;
#line 6 "cpp/z_test/yosupo-inverse_matrix.test.cpp"
#line 1 "cpp/math/matrix.cpp"
template <typename T>
struct mat{
vector<vector<T>> x;
int h,w;
mat():x(vector<vector<T>>()){}
mat(int h,int w):x(vector<vector<T>>(h,vector<T>(w))),h(h),w(w){}
mat(int h,int w, T c):x(vector<vector<T>>(h,vector<T>(w,c))),h(h),w(w){}
mat(vector<vector<T>> A):x(A),h(A.size()),w(A[0].size()){}
vector<T>& operator[](int i){return x[i];}
void resize(int h, int w){
x.assign(h, vector<T>(w, 0));
}
mat base(){
return mat(h,w,0);
}
mat& operator*=(mat& y){
mat<T> ret(h,y.w,0);
if(w != y.h){
for(int i = 0; h > i; i++){
for(int j = 0; y.w > j; j++){
ret[i][j] = -1;
}
}
}else{
for(int i = 0; h > i; i++){
for(int j = 0; y.w > j; j++){
for(int k = 0; w > k; k++){
ret[i][j] = ret[i][j] + x[i][k]*y[k][j];
}
}
}
}
for(int i = 0; h > i; i++){
x[i].resize(y.w);
}
w = y.w;
for(int i = 0; h > i; i++){
for(int j = 0; y.w > j; j++){
x[i][j] = ret[i][j];
}
}
return *this;
}
mat operator*(mat& y){return mat(*this) *= y;}
mat pow(long long n){//正方行列のみ
mat<T> res(h,w);
mat<T> ret(h,w,0);
mat<T> a(h,w);
for(int i = 0; h > i; i++){
ret[i][i] = 1;
}
for(int i = 0; h > i; i++){
for(int j = 0; w > j; j++){
a[i][j] = (*this)[i][j];
}
}
while(n > 0){
if(n & 1){
ret *= a;
}
a *= a;
n/=2;
}
for(int i = 0; h > i; i++){
for(int j = 0; w > j; j++){
res[i][j] = ret[i][j];
}
}
return res;
}
// Requirement: h==w
pair<bool, mat> inv(){
if(h != w)return {false, base()};
mat<T> gaussianMat(h, 2*w, 0);
for(int i = 0; h > i; i++){
for(int j = 0; w > j; j++){
gaussianMat[i][j] = (*this)[i][j];
}
}
for(int i = 0; h > i; i++){
gaussianMat[i][w+i] = 1;
}
for(int i = 0; h > i; i++){
for(int j = i; h > j; j++){
if(gaussianMat[j][i] != 0){
swap(gaussianMat[i], gaussianMat[j]);
}
}
T initCoeffient = gaussianMat[i][i];
if(initCoeffient == 0){
return {false, base()};
}
for(int j = 0; 2*w > j; j++){
gaussianMat[i][j] /= initCoeffient;
}
for(int j = i+1; h > j; j++){
T deleteCoeffient = gaussianMat[j][i] * -1;
for(int k = i; 2*w > k; k++){
gaussianMat[j][k] += deleteCoeffient * gaussianMat[i][k];
}
}
}
for(int i = 0; h > i; i++){
if(gaussianMat[i][i] != 1){
T normarizeCoeffient = gaussianMat[i][i];
if(normarizeCoeffient == 0)continue;
for(int j = i; 2*w > j; j++){
gaussianMat[i][j] /= normarizeCoeffient;
}
}
}
for(int i = h-1; 0 <= i; i--){
for(int j = 0; i > j; j++){
T deleteCoeffient = gaussianMat[j][i] * -1;
for(int k = i; 2*w > k; k++){
gaussianMat[j][k] += deleteCoeffient * gaussianMat[i][k];
}
}
}
mat v(h, w);
for(int i = 0; h > i; i++){
for(int j = 0; w > j; j++){
v[i][j] = gaussianMat[i][j+w];
}
}
return {true, v};
}
friend istream &operator>>(istream &is, mat &m){
for(int i = 0; m.h > i; i++){
for(int j = 0; m.w > j; j++){
is>>m.x[i][j];
}
}
return is;
}
friend ostream &operator<<(ostream &os, const mat &m){
for(int i = 0; m.h > i; i++){
for(int j = 0; m.w > j; j++){
os << m.x[i][j];
if(j+1 != m.w)cout << " ";
}
if(i+1 != m.h)cout << "\n";
}
return os;
}
};
#line 8 "cpp/z_test/yosupo-inverse_matrix.test.cpp"
int main(){
int n;cin>>n;
mat<mint> A(n,n);
cin >> A;
auto z = A.inv();
if(!z.first) cout << -1 << endl;
else cout << z.second << endl;
return 0;
}
cpp/z_test/yosupo-inverse_matrix.test.cpp
cpp/geometry/two-points-distance.cpp