結果
| 問題 | No.2503 Typical Path Counting Problem on a Grid |
| ユーザー |
 KumaTachiRen
|
| 提出日時 | 2023-10-13 21:50:15 |
| 言語 | C# (.NET 8.0.203) |
| 結果 |
AC
|
| 実行時間 | 1,599 ms / 2,000 ms |
| コード長 | 19,243 bytes |
| コンパイル時間 | 16,756 ms |
| コンパイル使用メモリ | 167,304 KB |
| 実行使用メモリ | 255,208 KB |
| 最終ジャッジ日時 | 2024-09-15 17:30:48 |
| 合計ジャッジ時間 | 26,551 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 206 ms
64,256 KB |
| testcase_01 | AC | 332 ms
74,496 KB |
| testcase_02 | AC | 212 ms
65,628 KB |
| testcase_03 | AC | 774 ms
87,524 KB |
| testcase_04 | AC | 1,279 ms
91,620 KB |
| testcase_05 | AC | 609 ms
87,776 KB |
| testcase_06 | AC | 1,596 ms
91,776 KB |
| testcase_07 | AC | 1,599 ms
91,648 KB |
| testcase_08 | AC | 951 ms
91,504 KB |
| testcase_09 | AC | 1,297 ms
255,208 KB |
コンパイルメッセージ
復元対象のプロジェクトを決定しています... /home/judge/data/code/main.csproj を復元しました (102 ms)。 MSBuild のバージョン 17.9.6+a4ecab324 (.NET) main -> /home/judge/data/code/bin/Release/net8.0/main.dll main -> /home/judge/data/code/bin/Release/net8.0/publish/
ソースコード
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;
using ModInt = StaticModInt<Mod998244353>;
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()
{
const int n_max = 10001000;
var a = new ModInt[n_max];
a[0] = 1;
a[1] = 2;
for (int i = 2; i < n_max; i++) a[i] = (i - 1) * a[i - 2] + 2 * i * a[i - 1];
int t = ri;
while (t-- > 0)
{
long n = rl, m = rl;
if (n > m) Swap(ref n, ref m);
if (n == 0)
{
Write(1);
continue;
}
if (n == m)
{
Write(a[n] * a[n] + a[n - 1] * a[n - 1] * n);
continue;
}
var pow = new Matrix<Mod998244353>(2, 2);
pow[0, 0] = 1; pow[1, 1] = 1;
var mat = new Matrix<Mod998244353>(2, 2);
mat[0, 1] = 1;
mat[1, 0] = n;
mat[1, 1] = 2 * n + 1;
long k = m - n;
while (k > 0)
{
if (k % 2 == 1) pow *= mat;
mat *= mat;
k /= 2;
}
ModInt ans = 0;
ans += (a[n - 1] * pow[0, 0] + a[n] * pow[0, 1]) * n * a[n - 1];
ans += (a[n - 1] * pow[1, 0] + a[n] * pow[1, 1]) * a[n];
Write(ans);
}
}
const long INF = 1L << 60;
int ri { [MethodImpl(256)] get => (int)sc.Integer(); }
(int, int) ri2 { [MethodImpl(256)] get => (ri, ri); }
(int, int, int) ri3 { [MethodImpl(256)] get => (ri, ri, ri); }
(int, int, int, int) ri4 { [MethodImpl(256)] get => (ri, ri, ri, ri); }
(int, int, int, int, int) ri5 { [MethodImpl(256)] get => (ri, ri, ri, ri, ri); }
long rl { [MethodImpl(256)] get => sc.Integer(); }
(long, long) rl2 { [MethodImpl(256)] get => (rl, rl); }
(long, long, long) rl3 { [MethodImpl(256)] get => (rl, rl, rl); }
(long, long, long, long) rl4 { [MethodImpl(256)] get => (rl, rl, rl, rl); }
(long, long, long, long, long) rl5 { [MethodImpl(256)] get => (rl, rl, rl, rl, rl); }
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());
}
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 (long x, long y, long g) ExtGcd(long a, long b) { if (b == 0) return (Sign(a), 0, Math.Abs(a)); long c = SafeMod(a, b); var (x2, y2, g) = ExtGcd(b, c); long x = SafeMod(y2, b); long y = (g - a * x) / b; return (x, y, g); } [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<T>(ref T x, ref T y) { T t = y; y = x; x = t; } [MethodImpl(256)] public static T Clamp<T>(T x, T l, T r) where T : IComparable<T> => x.CompareTo(l) <= 0 ? l : (x.CompareTo(r) <= 0 ? x : r); [MethodImpl(256)] public static T Clamp<T>(ref T x, T l, T r) where T : IComparable<T> => x = x.CompareTo(l) <= 0 ? l : (x.CompareTo(r) <= 0 ? x : r); [MethodImpl(256)] public static void Chmin<T>(ref T x, T y) where T : IComparable<T> { if (x.CompareTo(y) > 0) x = y; } [MethodImpl(256)] public static void Chmax<T>(ref T x, T y) where T : IComparable<T> { if (x.CompareTo(y) < 0) x = y; } [MethodImpl(256)] public static int LowerBound(long[] arr, long val, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), t => Sign(t - val), l, r); [MethodImpl(256)] public static int LowerBound(int[] arr, int val, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), t => t - val, l, r); [MethodImpl(256)] public static int LowerBound<T>(T[] arr, T val, int l = -1, int r = -1) where T : IComparable<T> => LowerBound(arr.AsSpan(), t => t.CompareTo(val), l, r); [MethodImpl(256)] public static int LowerBound<T>(T[] arr, Func<T, int> comp, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), comp, l, r); [MethodImpl(256)] public static int LowerBound<T>(Span<T> data, Func<T, int> 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(256)] 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(256)] 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<T>(string s, IEnumerable<T> t) => Console.WriteLine(string.Join(s, t)); [MethodImpl(256)] public static void WriteMat<T>(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>(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"); }
public interface IStaticMod { uint Mod { get; } bool IsPrime { get; } } public readonly struct Mod1000000007 : IStaticMod { public uint Mod => 1000000007; public bool IsPrime => true; } public readonly struct Mod998244353 : IStaticMod { public uint Mod => 998244353; public bool IsPrime => true; } public readonly struct StaticModInt<T> : IEquatable<StaticModInt<T>> where T : struct, IStaticMod { internal readonly uint _v; private static readonly T op = default; public int Value => (int)_v; public static int Mod => (int)op.Mod; public static StaticModInt<T> Zero => default; public static StaticModInt<T> One => new StaticModInt<T>(1u); [MethodImpl(256)] public static StaticModInt<T> Raw(int v) { var u = unchecked((uint)v); return new StaticModInt<T>(u); } [MethodImpl(256)] public StaticModInt(long v) : this(Round(v)) { } [MethodImpl(256)] public StaticModInt(ulong v) : this((uint)(v % op.Mod)) { } [MethodImpl(256)] private StaticModInt(uint v) => _v = v; [MethodImpl(256)] private static uint Round(long v) { var x = v % op.Mod; if (x < 0) x += op.Mod; return (uint)x; } [MethodImpl(256)] public static StaticModInt<T> operator ++(StaticModInt<T> v) { var x = v._v + 1; if (x == op.Mod) x = 0; return new StaticModInt<T>(x); } [MethodImpl(256)] public static StaticModInt<T> operator --(StaticModInt<T> v) { var x = v._v; if (x == 0) x = op.Mod; return new StaticModInt<T>(x - 1); } [MethodImpl(256)] public static StaticModInt<T> operator +(StaticModInt<T> lhs, StaticModInt<T> rhs) { var v = lhs._v + rhs._v; if (v >= op.Mod) v -= op.Mod; return new StaticModInt<T>(v); } [MethodImpl(256)] public static StaticModInt<T> operator -(StaticModInt<T> lhs, StaticModInt<T> rhs) { unchecked { var v = lhs._v - rhs._v; if (v >= op.Mod) v += op.Mod; return new StaticModInt<T>(v); } } [MethodImpl(256)] public static StaticModInt<T> operator *(StaticModInt<T> lhs, StaticModInt<T> rhs) => new StaticModInt<T>((uint)((ulong)lhs._v * rhs._v % op.Mod)); [MethodImpl(256)] public static StaticModInt<T> operator /(StaticModInt<T> lhs, StaticModInt<T> rhs) => new StaticModInt<T>((uint)((ulong)lhs._v * Inv(rhs._v) % op.Mod)); [MethodImpl(256)] public static StaticModInt<T> operator +(StaticModInt<T> v) => v; [MethodImpl(256)] public static StaticModInt<T> operator -(StaticModInt<T> v) => new StaticModInt<T>(v._v == 0 ? 0 : op.Mod - v._v); [MethodImpl(256)] public static bool operator ==(StaticModInt<T> lhs, StaticModInt<T> rhs) => lhs._v == rhs._v; [MethodImpl(256)] public static bool operator !=(StaticModInt<T> lhs, StaticModInt<T> rhs) => lhs._v != rhs._v; [MethodImpl(256)] public static implicit operator StaticModInt<T>(int v) => new StaticModInt<T>(v); [MethodImpl(256)] public static implicit operator StaticModInt<T>(uint v) => new StaticModInt<T>((long)v); [MethodImpl(256)] public static implicit operator StaticModInt<T>(long v) => new StaticModInt<T>(v); [MethodImpl(256)] public static implicit operator StaticModInt<T>(ulong v) => new StaticModInt<T>(v); [MethodImpl(256)] public static implicit operator long(StaticModInt<T> v) => v._v; [MethodImpl(256)] public static implicit operator ulong(StaticModInt<T> v) => v._v; [MethodImpl(256)] public StaticModInt<T> Pow(long n) { var x = this; var r = new StaticModInt<T>(1U); while (n > 0) { if ((n & 1) > 0) r *= x; x *= x; n >>= 1; } return r; } [MethodImpl(256)] public StaticModInt<T> Inv() => new StaticModInt<T>(Inv(_v)); [MethodImpl(256)] static ulong Inv(ulong x) { long u = op.Mod, xu = 1, yu = 0, v = (long)x, xv = 0, yv = 1; while (v != 0) { long w = SafeMod(u, v); long q = (u - w) / v; long xw = xu - xv * q; long yw = yu - yv * q; u = v; xu = xv; yu = yv; v = w; xv = xw; yv = yw; } return (ulong)(yu < 0 ? yu + op.Mod : yu); } [MethodImpl(256)] static long SafeMod(long x, long m) { long r = x % m; if (r < 0) r += m; return r; } [MethodImpl(256)] public override string ToString() => _v.ToString(); [MethodImpl(256)] public string ToString(string format, IFormatProvider formatProvider) => _v.ToString(format, formatProvider); [MethodImpl(256)] public override bool Equals(object obj) => obj is StaticModInt<T> m && Equals(m); [MethodImpl(256)] public bool Equals(StaticModInt<T> other) => _v == other._v; [MethodImpl(256)] public override int GetHashCode() => _v.GetHashCode(); }
public struct Matrix<Mod> where Mod : struct, IStaticMod { public int Height { get; private set; } public int Width { get; private set; } int size; StaticModInt<Mod>[] mat; [MethodImpl(256)] int GetIndex(int i, int j) => Width * i + j; [MethodImpl(256)] public StaticModInt<Mod> Get(int i, int j) => mat[GetIndex(i, j)]; [MethodImpl(256)] public StaticModInt<Mod> Set(int i, int j, StaticModInt<Mod> v) => mat[GetIndex(i, j)] = v; public StaticModInt<Mod> this[int i, int j] { [MethodImpl(256)] get => mat[GetIndex(i, j)]; [MethodImpl(256)] set => mat[GetIndex(i, j)] = value; } public Matrix(int n, int m) { Height = n; Width = m; size = n * m; mat = new StaticModInt<Mod>[size]; } public Matrix(StaticModInt<Mod>[,] _mat) { Height = _mat.GetLength(0); Width = _mat.GetLength(1); size = Height * Width; mat = new StaticModInt<Mod>[size]; for (int i = 0; i < Height; i++) for (int j = 0; j < Width; j++) mat[GetIndex(i, j)] = _mat[i, j]; } public Matrix(Matrix<Mod> _mat) { Height = _mat.Height; Width = _mat.Width; size = _mat.size; mat = (StaticModInt<Mod>[])_mat.mat.Clone(); } public override string ToString() { if (Height == 0 || Width == 0) return ""; var lines = new string[Height]; for (int i = 0; i < Height; i++) { var line = new string[Width]; for (int j = 0; j < Width; j++) line[j] = Get(i, j).ToString(); lines[i] = string.Join(" ", line); } return string.Join("\n", lines); } public static Matrix<Mod> operator +(Matrix<Mod> a, Matrix<Mod> b) { Contract.Requires(a.Height == b.Height && a.Width == b.Width); var c = new Matrix<Mod>(a); for (int i = 0; i < b.size; i++) c.mat[i] += b.mat[i]; return c; } public static Matrix<Mod> operator -(Matrix<Mod> a, Matrix<Mod> b) { Contract.Requires(a.Height == b.Height && a.Width == b.Width); var c = new Matrix<Mod>(a); for (int i = 0; i < b.size; i++) c.mat[i] -= b.mat[i]; return c; } public static Matrix<Mod> operator *(Matrix<Mod> a, Matrix<Mod> b) { Contract.Requires(a.Width == b.Height); var c = new Matrix<Mod>(a.Height, b.Width); for (int i = 0; i < a.Height; i++) for (int k = 0; k < a.Width; k++) for (int j = 0; j < b.Width; j++) c.mat[c.GetIndex(i, j)] += a.mat[a.GetIndex(i, k)] * b.mat[b.GetIndex(k, j)]; return c; } [MethodImpl(256)] public void SwapRows(int u, int v) { StaticModInt<Mod> tmp; for (int i = 0; i < Width; i++) { tmp = this[u, i]; this[u, i] = this[v, i]; this[v, i] = tmp; } } [MethodImpl(256)] public void SwapColumns(int u, int v) { StaticModInt<Mod> tmp; for (int i = 0; i < Height; i++) { tmp = this[i, u]; this[i, u] = this[i, v]; this[i, v] = tmp; } } [MethodImpl(256)] public StaticModInt<Mod> Determinant() { Contract.Requires(Height == Width); int n = Height; var a = new Matrix<Mod>(this); StaticModInt<Mod> det = 1, inv, coeff; for (int y = 0; y < n - 1; y++) { if (a[y, y] == 0) { int z = y + 1; for (; z < n; z++) if (a[z, y] != 0) break; if (z == n) return 0; a.SwapRows(y, z); det = -det; } inv = a[y, y].Inv(); for (int x = y + 1; x < n; x++) { coeff = a[x, y] * inv; for (int z = y; z < n; z++) a[x, z] -= coeff * a[y, z]; } det *= a[y, y]; } det *= a[n - 1, n - 1]; return det; } [MethodImpl(256)] public (int rank, Matrix<Mod> mat) RowReduction() { int n = Height, m = Width; var a = new Matrix<Mod>(this); StaticModInt<Mod> inv, coeff; int rank = 0; for (int k = 0; k < m && rank < n; k++) { if (a[rank, k] == 0) { int y = rank + 1; for (; y < n; y++) if (a[y, k] != 0) break; if (y == n) continue; a.SwapRows(rank, y); } inv = a[rank, k].Inv(); for (int j = k; j < m; j++) a[rank, j] *= inv; for (int i = 0; i < n; i++) { if (i == rank) continue; coeff = a[i, k]; for (int j = k; j < m; j++) a[i, j] -= coeff * a[rank, j]; } rank++; } return (rank, a); } [MethodImpl(256)] public (bool exist, Matrix<Mod> mat) Inverse() { Contract.Requires(Height == Width); int n = Height; var a = new Matrix<Mod>(n, n + n); for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) a[i, j] = this[i, j]; for (int i = 0; i < n; i++) a[i, n + i] = 1; var red = a.RowReduction(); if (red.rank < n) return (false, default); bool ok = true; for (int i = 0; ok && i < n; i++) ok &= red.mat[i, i] == 1; if (!ok) return (false, default); a = new Matrix<Mod>(n, n); for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) a[i, j] = red.mat[i, j + n]; return (true, a); } }