#include <cmath>
#include <cassert>
#include <cstdlib>
#include <iostream>
#include <sstream>

using namespace std;

// single Jacobi iteration step
double single_jacobi_iteration(double** A, double** B, int n, int m) {
   for (int i = 1; i <= n; ++i) {
      for (int j = 1; j <= m; ++j) {
	 B[i][j] = 0.25 * (A[i-1][j] + A[i][j-1] + A[i][j+1] + A[i+1][j]);
      }
   }
   double maxdiff = 0;
   for (int i = 1; i <= n; ++i) {
      for (int j = 1; j <= m; ++j) {
	 double diff = fabs(A[i][j] - B[i][j]);
	 if (diff > maxdiff) maxdiff = diff;
	 A[i][j] = B[i][j];
      }
   }
   return maxdiff;
}

void initialize_A(double& Aij, int i, int j, int N) {
   const static double E_POWER_MINUS_PI = pow(M_E, -M_PI);
   if (j == 0) {
      Aij = sin(M_PI * ((double)i/(N-1)));
   } else if (j == N-1) {
      Aij = sin(M_PI * ((double)i/(N-1))) * E_POWER_MINUS_PI;
   } else {
      Aij = 0;
   }
}

double** run_jacobi_iteration(int N, double eps) {
   int n = N-2;
   double** A = new double*[N]; assert(A);
   for (int i = 0; i < N; ++i) {
      A[i] = new double[N]; assert(A[i]);
      for (int j = 0; j < N; ++j) {
	 initialize_A(A[i][j], i, j, N);
      }
   }
   double** B = new double*[N-1];
   for (int i = 1; i < N-1; ++i) {
      B[i] = new double[N-1]; assert(B[i]);
   }

   double maxdiff;
   do {
      maxdiff = single_jacobi_iteration(A, B, n, n);
   } while (maxdiff > eps);

   for (int i = 1; i < N-1; ++i) {
      delete[] B[i];
   }
   delete[] B;

   return A;
}

char* cmdname;
void usage() {
   cerr << "Usage: " << cmdname << " [N [eps]] " << endl;
   exit(1);
}

int main(int argc, char** argv) {
   int N = 10;
   double eps = 1e-6;

   cmdname = *argv++; --argc;
   if (argc > 2) usage();
   if (argc > 0) {
      istringstream arg(*argv++); --argc;
      if (!(arg >> N) || N < 3) usage();
   }
   if (argc > 0) {
      istringstream arg(*argv++); --argc;
      if (!(arg >> eps) || eps <= 0) usage();
   }
   cout << N << endl;
   double** A = run_jacobi_iteration(N, eps);
   for (int i = 0; i < N; ++i) {
      for (int j = 0; j < N; ++j) {
	 cout << " " << A[i][j];
      }
      cout << endl;
      delete[] A[i];
   }
   delete[] A;
}