import numpy as np
import sys
import scipy.linalg
import sympy

###INPUT

# c = 0
# for number, line in enumerate(sys.stdin):
#     if number == 0:
#         q = line.split(' ')[1]
#     if number == 1:
#         type_mat = line
#     if number > 1:
#         if c == 0:
#             line = line.split('\n')[0]
#             matrix = list(map(int, line))
#             matrix = np.mat(matrix)
#             c += 1
#         else:
#             line = line.split('\n')[0]
#             line_mat = list(map(int, line))
#             matrix = np.vstack((matrix, line_mat))

def gjel(A, p):
    """Gauss-Jordan elimination."""
    nulldim = 0
    for i, row1 in enumerate(A):
        pivot = A[i:, i].argmax() + i
        if A[pivot, i] == 0:
            nulldim = (len(A) - i) % p #####
            break
        new_row = (A[pivot] * A[pivot, i]) % p #####
        A[pivot] = A[i]
        row1[:] = new_row

        for j, row2 in enumerate(A):
            if j == i:
                continue
            row2[:] = (row2[:] - new_row*A[j, i]) % p ####
    return A, nulldim

def transforms(matrix, field):
    k, n = matrix.shape
    matrix = gjel(matrix, p=field)[0]
    new_matrix = np.hstack((-matrix[:,k:].T, np.diag([1]*(n-k))) ) % field

    return new_matrix

q = int(q)


if type_mat.split(' ')[0] == 'parity':
    H = matrix
    G = transforms(matrix=matrix, field=q)
    d = len(sympy.Matrix(H).T.rref()[1])
    print('distance: ' + str(d))
    print('generator matrix:')
    for strng in range(G.shape[0]):
        print(''.join([str(i) for i in np.array(G[strng]).flatten()]))



if type_mat.split(' ')[0] == 'generator':
    G = matrix
    H = transforms(matrix=matrix, field=q)
    d = len(sympy.Matrix(H).T.rref()[1])
    print('distance: ' + str(d))
    print('parity check matrix:')
    for strng in range(H.shape[0]):
        print(''.join([str(i) for i in np.array(H[strng]).flatten()]))