#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; //ll mod = 1; constexpr ll mod = 998244353; //constexpr ll mod = 1000000007; const int mod17 = 1000000007; const ll INF = mod * mod; typedef pairP; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; using ld = double; typedef pair LDP; const ld eps = 1e-10; const ld pi = acosl(-1.0); template void chmin(T& a, T b) { a = min(a, b); } template void chmax(T& a, T b) { a = max(a, b); } template vector vmerge(vector& a, vector& b) { vector res; int ida = 0, idb = 0; while (ida < a.size() || idb < b.size()) { if (idb == b.size()) { res.push_back(a[ida]); ida++; } else if (ida == a.size()) { res.push_back(b[idb]); idb++; } else { if (a[ida] < b[idb]) { res.push_back(a[ida]); ida++; } else { res.push_back(b[idb]); idb++; } } } return res; } template void cinarray(vector& v) { rep(i, v.size())cin >> v[i]; } template void coutarray(vector& v) { rep(i, v.size()) { if (i > 0)cout << " "; cout << v[i]; } cout << "\n"; } ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; //if (x == 0)return 0; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } //mod should be <2^31 struct modint { int n; modint() :n(0) { ; } modint(ll m) { if (m < 0 || mod <= m) { m %= mod; if (m < 0)m += mod; } n = m; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } bool operator<(modint a, modint b) { return a.n < b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } const int max_n = 1 << 20; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } ll gcd(ll a, ll b) { a = abs(a); b = abs(b); if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } template void addv(vector& v, int loc, T val) { if (loc >= v.size())v.resize(loc + 1, 0); v[loc] += val; } /*const int mn = 2000005; bool isp[mn]; vector ps; void init() { fill(isp + 2, isp + mn, true); for (int i = 2; i < mn; i++) { if (!isp[i])continue; ps.push_back(i); for (int j = 2 * i; j < mn; j += i) { isp[j] = false; } } }*/ //[,val) template auto prev_itr(set& st, T val) { auto res = st.lower_bound(val); if (res == st.begin())return st.end(); res--; return res; } //[val,) template auto next_itr(set& st, T val) { auto res = st.lower_bound(val); return res; } using mP = pair; mP operator+(mP a, mP b) { return { a.first + b.first,a.second + b.second }; } mP operator+=(mP& a, mP b) { a = a + b; return a; } mP operator-(mP a, mP b) { return { a.first - b.first,a.second - b.second }; } mP operator-=(mP& a, mP b) { a = a - b; return a; } LP operator+(LP a, LP b) { return { a.first + b.first,a.second + b.second }; } LP operator+=(LP& a, LP b) { a = a + b; return a; } LP operator-(LP a, LP b) { return { a.first - b.first,a.second - b.second }; } LP operator-=(LP& a, LP b) { a = a - b; return a; } mt19937 mt(time(0)); const string drul = "DRUL"; string senw = "SENW"; //DRUL,or SENW //int dx[4] = { 1,0,-1,0 }; //int dy[4] = { 0,1,0,-1 }; //------------------------------------ void solve() { ll p; cin >> p; int n, m; cin >> n >> m; vector> a(n, vector(m)); rep(i, n) { rep(j, m)cin >> a[i][j]; } vector>> ans; if (n == 1 || m == 1) { ans.push_back(a); } else { auto mem = a; rep(i, n) { a[i].resize(n + m); a[i][i + m] = 1; } int le = 0; rep(j, m) { if (le == n)break; Rep(i, le, n) { if (a[i][j]) { swap(a[i], a[le]); break; } } if (a[le][j]) { ll rev = mod_pow(a[le][j], p - 2, p); for (int i = le + 1; i < n; i++) { ll coef = rev * a[i][j] % p; coef = (p - coef) % p; for (int k = j; k < n + m; k++) { a[i][k] += coef * a[le][k]; a[i][k] %= p; } } le++; } } if (le == 0) { vector> ans1(n); rep(i, n)ans1[i] = { 0 }; ans.push_back(ans1); vector> ans2(1); ans2[0].resize(m, 0); ans.push_back(ans2); } else if (le * (n + m) >= n * m) { ans.push_back(mem); } else { //rep(i, n)coutarray(a[i]); vector trans(n, -1); vector bs; rep(i, le)rep(j, n)if (a[i][j + m] != 0)bs.push_back(j); sort(all(bs)); bs.erase(unique(all(bs)), bs.end()); assert(bs.size() == le); bs.erase(unique(all(bs)), bs.end()); rep(j, bs.size())trans[bs[j]] = j; vector> ans2(le); rep(i, le)ans2[i] = mem[bs[i]]; vector> ans1(n, vector(le)); rep(i, n) { int id = -1; rep(j, n)if (a[i][j + m] == 1)if (trans[j] < 0) { id = j; } if (id >= 0) { rep(j, le)ans1[id][j] = (p - a[i][bs[j] + m]) % p; } } rep(i, bs.size())ans1[bs[i]][i] = 1; ans.push_back(ans1); ans.push_back(ans2); vector> t(n, vector(m)); rep(i, n)rep(j, le)rep(k, m) { t[i][k] += ans1[i][j] * ans2[j][k] % p; t[i][k] %= p; } //coutarray(bs); rep(i, n)rep(j, m)assert(t[i][j] == mem[i][j]); //rep(i, n)coutarray(t[i]); } } cout << ans.size() << "\n"; rep(i, ans.size()) { auto& sans = ans[i]; cout << sans.size() << " " << sans[0].size() << "\n"; rep(j, sans.size())coutarray(sans[j]); } } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed<> t; rep(i, t) solve(); return 0; }