using System; using System.ComponentModel; using System.Collections; using System.Collections.Generic; using System.Diagnostics; using System.Diagnostics.Contracts; using System.IO; using System.Linq; using System.Numerics; using System.Runtime.Intrinsics.X86; using System.Runtime.CompilerServices; using System.Runtime.InteropServices; using System.Text; using static Functions; using static OutputLib; static class Program { static public void Main(string[] args) { Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }); new Solver(); Console.Out.Flush(); } } public class Solver { public Solver() { Solve(); } void Solve() { int p = ri; int n = ri, m = ri; ModInt.Mod = p; var a = new ModInt[n][]; for (int i = 0; i < n; i++) { a[i] = new ModInt[m]; for (int j = 0; j < m; j++) a[i][j] = ri; } const bool debug = false; var r = Calc(a, n, m).ms; Write(r.Count); ModInt[][] prod = null; foreach (var b in r) { Write($"{b.Length} {b[0].Length}"); WriteMat(b); if (debug) { if (prod == null) prod = b; else prod = Mul(prod, b); } } if (debug) WriteMat(prod); } ModInt[][] Mul(ModInt[][] a, ModInt[][] b) { int l = a.Length; int n = b.Length; int m = b[0].Length; var c = new ModInt[l][]; for (int i = 0; i < l; i++) c[i] = new ModInt[m]; for (int i = 0; i < l; i++) for (int j = 0; j < m; j++) for (int k = 0; k < n; k++) c[i][j] += a[i][k] * b[k][j]; return c; } (int score, List ms) Calc(ModInt[][] a, int n, int m) { if (n == 1 || m == 1) return (n * m, new List() { a }); var rawa = new ModInt[n][]; for (int i = 0; i < n; i++) { rawa[i] = new ModInt[m]; for (int j = 0; j < m; j++) rawa[i][j] = a[i][j]; } var f = new bool[n]; var coeff = new List(); var basis = new List(); for (int k = 0; k < m; k++) { int x = 0; while (x < n && (f[x] || a[x][k] == 0)) x++; if (x == n) break; f[x] = true; ModInt inv = a[x][k].Inv(); var cs = new ModInt[n]; for (int i = 0; i < n; i++) { if (i == x) { cs[i] = 1; continue; } if (f[i]) continue; ModInt c = a[i][k] * inv; cs[i] = c; for (int j = 0; j < m; j++) a[i][j] -= a[x][j] * c; } coeff.Add(cs); basis.Add(a[x]); } int dim = basis.Count; if (dim == 0) { basis.Add(new ModInt[m]); coeff.Add(new ModInt[n]); dim++; } if (dim == Math.Min(n, m)) { return (n * m, new List { rawa }); } var b = new ModInt[n][]; for (int i = 0; i < n; i++) { b[i] = new ModInt[dim]; for (int j = 0; j < dim; j++) b[i][j] = coeff[j][i]; } var res1 = Calc(b, n, dim); var res2 = Calc(basis.ToArray(), dim, m); if (res1.score + res2.score < m * n) { var ret = res1.ms; foreach (var mat in res2.ms) ret.Add(mat); return (res1.score + res2.score, ret); } else { return (n * m, new List { rawa }); } } const long INF = 1L << 60; int ri { [MethodImpl(256)] get => (int)sc.Integer(); } long rl { [MethodImpl(256)] get => sc.Integer(); } uint rui { [MethodImpl(256)] get => (uint)sc.UInteger(); } ulong rul { [MethodImpl(256)] get => sc.UInteger(); } double rd { [MethodImpl(256)] get => sc.Double(); } string rs { [MethodImpl(256)] get => sc.Scan(); } string rline { [MethodImpl(256)] get => sc.Line(); } public StreamScanner sc = new StreamScanner(Console.OpenStandardInput()); } struct ModInt { public static long Mod = 998244353; public long Val { get; private set; } public ModInt(long v) { Val = SafeMod(v, Mod); } public override string ToString() { return Val.ToString(); } public override bool Equals(object obj) => obj is ModInt other && this.Equals(other); public bool Equals(ModInt x) => Val == x.Val; public override int GetHashCode() => Val.GetHashCode(); public static bool operator ==(ModInt a, ModInt b) { return a.Val == b.Val; } public static bool operator !=(ModInt a, ModInt b) { return a.Val != b.Val; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static implicit operator ModInt(long n) => new ModInt(SafeMod(n, Mod)); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator +(ModInt a, ModInt b) { long r = a.Val + b.Val; return new ModInt(r < Mod ? r : r - Mod); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator -(ModInt a, ModInt b) { long r = a.Val - b.Val; return new ModInt(r < 0 ? r + Mod : r); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator -(ModInt a) => new ModInt(a.Val == 0 ? 0 : Mod - a.Val); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator *(ModInt a, ModInt b) => new ModInt(a.Val * b.Val % Mod); [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt operator /(ModInt a, ModInt b) => a * b.Inv(); [MethodImpl(MethodImplOptions.AggressiveInlining)] public ModInt Pow(long n) { long t = Val, r = 1; while (n > 0) { if ((n & 1) == 1) r = r * t % Mod; t = t * t % Mod; n >>= 1; } return new ModInt(r); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public ModInt Inv() => Gcd(Val, Mod).x; [MethodImpl(MethodImplOptions.AggressiveInlining)] private static (long x, long y, long g) Gcd(long a, long b) { if (b == 0) return a >= 0 ? (1, 0, a) : (-1, 0, -a); long c = a % b; if (c < 0) c += b; var r = Gcd(b, c); long x = SafeMod(r.y, b); long g = r.g; long y = (g - a * x) / b; return (x, y, g); } [MethodImpl(MethodImplOptions.AggressiveInlining)] private static long SafeMod(long x, long m) { long r = x % m; return r < 0 ? r + m : r; } } public static class Functions { [MethodImpl(256)] public static int Popcount(ulong x) { x = (x & 0x5555555555555555UL) + ((x >> 1) & 0x5555555555555555UL); x = (x & 0x3333333333333333UL) + ((x >> 2) & 0x3333333333333333UL); x = (x & 0x0f0f0f0f0f0f0f0fUL) + ((x >> 4) & 0x0f0f0f0f0f0f0f0fUL); x = (x & 0x00ff00ff00ff00ffUL) + ((x >> 8) & 0x00ff00ff00ff00ffUL); x = (x & 0x0000ffff0000ffffUL) + ((x >> 16) & 0x0000ffff0000ffffUL); x = (x & 0x00000000ffffffffUL) + ((x >> 32) & 0x00000000ffffffffUL); return (int)x; } [MethodImpl(256)] public static int Popcount(int x) { x = (x & 0x55555555) + ((x >> 1) & 0x55555555); x = (x & 0x33333333) + ((x >> 2) & 0x33333333); x = (x & 0x0f0f0f0f) + ((x >> 4) & 0x0f0f0f0f); x = (x & 0x00ff00ff) + ((x >> 8) & 0x00ff00ff); x = (x & 0x0000ffff) + ((x >> 16) & 0x0000ffff); return x; } [MethodImpl(256)] public static int Ctz(long x) { if (x == 0) return -1; return Popcount((ulong)((x & -x) - 1)); } [MethodImpl(256)] public static int CeilPow2(int n) { int x = 0; while ((1 << x) < n) x++; return x; } [MethodImpl(256)] public static int SafeMod(int x, int m) { int r = x % m; return r < 0 ? r + Math.Abs(m) : r; } [MethodImpl(256)] public static long SafeMod(long x, long m) { long r = x % m; return r < 0 ? r + Math.Abs(m) : r; } [MethodImpl(256)] public static int Sign(long x) => x == 0 ? 0 : (x < 0 ? -1 : 1); [MethodImpl(256)] public static int Sign(double x) => x == 0 ? 0 : (x < 0 ? -1 : 1); [MethodImpl(256)] public static int DigitSum(long n, int d = 10) { long s = 0; while (n > 0) { s += n % d; n /= d; } return (int)s; } [MethodImpl(256)] public static long Floor(long a, long b) => a >= 0 ? a / b : (a + 1) / b - 1; [MethodImpl(256)] public static long Ceil(long a, long b) => a > 0 ? (a - 1) / b + 1 : a / b; [MethodImpl(256)] public static int Gcd(int a, int b) => b == 0 ? a : Gcd(b, a % b); [MethodImpl(256)] public static long Gcd(long a, long b) => b == 0 ? a : Gcd(b, a % b); [MethodImpl(256)] public static void Swap(ref int x, ref int y) { x ^= y; y ^= x; x ^= y; } [MethodImpl(256)] public static void Swap(ref long x, ref long y) { x ^= y; y ^= x; x ^= y; } [MethodImpl(256)] public static void Swap(ref T x, ref T y) { T t = y; y = x; x = t; } [MethodImpl(256)] public static T Clamp(T x, T l, T r) where T : IComparable => x.CompareTo(l) <= 0 ? l : (x.CompareTo(r) <= 0 ? x : r); [MethodImpl(256)] public static T Clamp(ref T x, T l, T r) where T : IComparable => x = x.CompareTo(l) <= 0 ? l : (x.CompareTo(r) <= 0 ? x : r); [MethodImpl(256)] public static void Chmin(ref T x, T y) where T : IComparable { if (x.CompareTo(y) > 0) x = y; } [MethodImpl(256)] public static void Chmax(ref T x, T y) where T : IComparable { if (x.CompareTo(y) < 0) x = y; } public static int LowerBound(long[] arr, long val, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), t => Sign(t - val), l, r); public static int LowerBound(int[] arr, int val, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), t => t - val, l, r); public static int LowerBound(T[] arr, Func comp, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), comp, l, r); public static int LowerBound(Span data, Func comp, int l = -1, int r = -1) { if (data.Length == 0) return -1; if (l == -1) l = 0; if (r == -1) r = data.Length; while (l < r) { int x = (l + r) / 2; if (comp(data[x]) < 0) l = x + 1; else r = x; } return l; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static string ToBase2(long v, int digit = -1) { if (digit == -1) { digit = 0; while ((v >> digit) > 0) digit++; } var c = new string[digit]; for (int i = 0; i < digit; i++) c[digit - 1 - i] = ((v >> i) & 1) == 0 ? "0" : "1"; return string.Join("", c); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static string ToBaseN(long v, int n, int digit = -1) { if (digit == -1) { digit = 0; long pow = 1; while (v >= pow) { digit++; pow *= n; } } var c = new int[digit]; for (int i = 0; i < digit; i++, v /= n) c[digit - 1 - i] = (int)(v % n); return string.Join("", c); } } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } private readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } [MethodImpl(256)] private byte read() { if (isEof) throw new EndOfStreamException(); if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; } [MethodImpl(256)] public char Char() { byte b = 0; do b = read(); while (b < 33 || 126 < b); return (char)b; } [MethodImpl(256)] public string Line() { var sb = new StringBuilder(); for (var b = Char(); b != 10 && !isEof; b = (char)read()) sb.Append(b); return sb.ToString(); } [MethodImpl(256)] public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } [MethodImpl(256)] public long Integer() { long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != '-' && (b < '0' || '9' < b)); if (b == '-') { ng = true; b = read(); } for (; true; b = read()) { if (b < '0' || '9' < b) return ng ? -ret : ret; else ret = ret * 10 + b - '0'; } } [MethodImpl(256)] public ulong UInteger() { ulong ret = 0; byte b = 0; do b = read(); while (b < '0' || '9' < b); for (; true; b = read()) { if (b < '0' || '9' < b) return ret; else ret = ret * 10 + b - '0'; } } [MethodImpl(256)] public double Double() => double.Parse(Scan()); } public static class OutputLib { [MethodImpl(256)] public static void WriteJoin(string s, IEnumerable t) => Console.WriteLine(string.Join(s, t)); [MethodImpl(256)] public static void WriteMat(T[,] a) { int sz1 = a.GetLength(0); int sz2 = a.GetLength(1); for (int i = 0; i < sz1; i++) { var b = new T[sz2]; for (int j = 0; j < sz2; j++) b[j] = a[i, j]; WriteJoin(" ", b); } } [MethodImpl(256)] public static void WriteMat(T[][] a) { for (int i = 0; i < a.Length; i++) WriteJoin(" ", a[i]); } [MethodImpl(256)] public static void Write(object t) => Console.WriteLine(t.ToString()); [MethodImpl(256)] public static void Write(string str) => Console.WriteLine(str); [MethodImpl(256)] public static void Write(string str, object arg1) => Console.WriteLine(str, arg1); [MethodImpl(256)] public static void Write(string str, object arg1, object arg2) => Console.WriteLine(str, arg1, arg2); [MethodImpl(256)] public static void Write(string str, object arg1, object arg2, object arg3) => Console.WriteLine(str, arg1, arg2, arg3); [MethodImpl(256)] public static void Write(string str, params object[] arg) => Console.WriteLine(str, arg); [MethodImpl(256)] public static void WriteFlush(object t) { Console.WriteLine(t.ToString()); Console.Out.Flush(); } [MethodImpl(256)] public static void WriteError(object t) => Console.Error.WriteLine(t.ToString()); [MethodImpl(256)] public static void Flush() => Console.Out.Flush(); [MethodImpl(256)] public static void YN(bool t) => Console.WriteLine(t ? "YES" : "NO"); [MethodImpl(256)] public static void Yn(bool t) => Console.WriteLine(t ? "Yes" : "No"); [MethodImpl(256)] public static void yn(bool t) => Console.WriteLine(t ? "yes" : "no"); }