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#include <mpi.h>
#include <vector>

// A function to perform local matrix multiplication.
void local_matrix_multiply(const std::vector<int>& A, const std::vector<int>& B, std::vector<int>& C, int block_size) {
    // Implement your matrix multiplication logic here.
    // For example, a simple triple nested loop for matrix multiplication.
}

int main(int argc, char* argv[]) {
    MPI_Init(&argc, &argv);

    // Assuming we have Px * Px * Pz processors and square matrices of size N
    const int Px = 2; // Number of processors in each row/column in a 2D layer
    const int Pz = 2; // Number of layers
    const int N = 4; // Matrix size (N x N)

    int rank, size;
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    MPI_Comm_size(MPI_COMM_WORLD, &size);

    // Validate our assumptions
    if(size != Px * Px * Pz) {
        if(rank == 0) {
            std::cerr << "The number of processors does not match Px * Px * Pz." << std::endl;
        }
        MPI_Finalize();
        return -1;
    }

    // Create 3D Cartesian topology for processors
    int dims[3] = {Px, Px, Pz};
    int periods[3] = {1, 1, 1}; // Enable wrapping for circular shifts
    MPI_Comm grid_comm;
    MPI_Cart_create(MPI_COMM_WORLD, 3, dims, periods, 1, &grid_comm);

    // Get new rank and coordinates in the grid
    int grid_rank, coords[3];
    MPI_Comm_rank(grid_comm, &grid_rank);
    MPI_Cart_coords(grid_comm, grid_rank, 3, coords);

    // Calculate block size for each processor
    int block_size = N / (Px * Pz); // Assuming N is evenly divisible by Px * Pz

    // Allocate memory for local blocks of A, B, and C
    std::vector<int> A_block(block_size * block_size, 0);
    std::vector<int> B_block(block_size * block_size, 0);
    std::vector<int> C_block(block_size * block_size, 0);

    // Distribute initial blocks of A and B to processors (omitted for brevity)
    // ...

    // Perform initial local matrix multiplication
    local_matrix_multiply(A_block, B_block, C_block, block_size);

    // Get rank of right and downward neighbors for A and B shifting
    int right_src, right_dst, down_src, down_dst;
    MPI_Cart_shift(grid_comm, 1, 1, &right_src, &right_dst); // Shift along the second dimension (j)
    MPI_Cart_shift(grid_comm, 0, 1, &down_src, &down_dst); // Shift along the first dimension (i)

    // Circular shift and local multiplication for Pz steps
    for(int step = 0; step < Pz; ++step) {
        // Circularly shift A rightwards and B downwards
        std::vector<int> A_recv(block_size * block_size), B_recv(block_size * block_size);
        MPI_Status status;

        // Shift A rightwards
        MPI_Sendrecv_replace(A_block.data(), block_size * block_size, MPI_INT, right_dst, 0, right_src, 0, grid_comm, &status);
        
        // Shift B downwards
        MPI_Sendrecv_replace(B_block.data(), block_size * block_size, MPI_INT, down_dst, 1, down_src, 1, grid_comm, &status);

        // Perform local matrix multiplication with the received blocks
        local_matrix_multiply(A_block, B_block, C_block, block_size);
    }

    // Gather the local C blocks into the global C matrix (omitted for brevity)
    // ...

    // Clean up
    MPI_Comm_free(&grid_comm);
    MPI_Finalize();

    return 0;
}