#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; using Int = long long; template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template ostream &operator<<(ostream &os, const vector &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; } template void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } //////////////////////////////////////////////////////////////////////////////// // Barrett struct ModInt { static unsigned M; static unsigned long long NEG_INV_M; static void setM(unsigned long long m) { M = m; NEG_INV_M = -1ULL / M; } unsigned x; ModInt() : x(0U) {} ModInt(unsigned x_) : x(x_ % M) {} ModInt(unsigned long long x_) : x(x_ % M) {} ModInt(int x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} ModInt(long long x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; } ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; } ModInt &operator*=(const ModInt &a) { const unsigned long long y = static_cast(x) * a.x; const unsigned long long q = static_cast((static_cast(NEG_INV_M) * y) >> 64); const unsigned long long r = y - M * q; x = r - M * (r >= M); return *this; } ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); } ModInt pow(long long e) const { if (e < 0) return inv().pow(-e); ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b; } ModInt inv() const { unsigned a = M, b = x; int y = 0, z = 1; for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast(q) * z; y = z; z = w; } assert(a == 1U); return ModInt(y); } ModInt operator+() const { return *this; } ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; } ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); } ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); } ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); } ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); } template friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); } template friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); } template friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); } template friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); } explicit operator bool() const { return x; } bool operator==(const ModInt &a) const { return (x == a.x); } bool operator!=(const ModInt &a) const { return (x != a.x); } friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; } }; unsigned ModInt::M; unsigned long long ModInt::NEG_INV_M; // !!!Use ModInt::setM!!! //////////////////////////////////////////////////////////////////////////////// // a \in Mat(m, n), rank(a) = r // b \in Mat(m, r), c \in Mat(r, n), a = b c // O(m n min(m, n)) // Call by value: Modifies a (Watch out when using C-style array!) template pair>, vector>> rankDecompose(vector> a) { assert(!a.empty()); const int m = a.size(), n = a[0].size(); vector is(m); for (int i = 0; i < m; ++i) is[i] = i; vector> b(m, vector(min(m, n), 0)); int r = 0; for (int h = 0; r < m && h < n; ++h) { for (int i = r; i < m; ++i) if (a[i][h]) { swap(a[r], a[i]); swap(is[r], is[i]); break; } if (a[r][h]) { const T s = a[r][h].inv(); for (int i = r + 1; i < m; ++i) { const T t = b[is[i]][r] = s * a[i][h]; for (int j = h; j < n; ++j) a[i][j] -= t * a[r][j]; } ++r; } } for (int i = 0; i < m; ++i) b[i].resize(r); for (int k = 0; k < r; ++k) b[is[k]][k] = 1; a.resize(r); return std::make_pair(b, a); } //////////////////////////////////////////////////////////////////////////////// using Mint = ModInt; int P, M, N; vector> A; int main() { for (; ~scanf("%d", &P); ) { Mint::setM(P); scanf("%d%d", &M, &N); A.assign(M, vector(N)); for (int i = 0; i < M; ++i) for (int j = 0; j < N; ++j) { scanf("%u", &A[i][j].x); } auto ans = rankDecompose(A); int r = ans.second.size(); if (r == 0) { r = 1; ans.first.assign(M, vector(r, 0)); ans.second.assign(r, vector(N, 0)); } if (M * N <= M * r + r * N) { puts("1"); printf("%d %d\n", M, N); for (int i = 0; i < M; ++i) { for (int j = 0; j < N; ++j) { if (j) printf(" "); printf("%u", A[i][j].x); } puts(""); } } else { puts("2"); printf("%d %d\n", M, r); for (int i = 0; i < M; ++i) { for (int j = 0; j < r; ++j) { if (j) printf(" "); printf("%u", ans.first[i][j].x); } puts(""); } printf("%d %d\n", r, N); for (int i = 0; i < r; ++i) { for (int j = 0; j < N; ++j) { if (j) printf(" "); printf("%u", ans.second[i][j].x); } puts(""); } } #ifdef LOCAL cerr<<"========"<