# https://www.codeconvert.ai/pascal-to-python-converter



import sys

def euler_path_cycle(n, a):
    # Calculate the degree of each node
    g = [0] * n
    for i in range(n):
        
        for j in range(n):
            g[i] += a[i][j]

    # Print the adjacency matrix
    print("Adjacency matrix:")
    for row in a:
        print(" ".join(map(str, row)))
    print()

    # Print the degree of each node
    print("Node degrees:")
    for degree in g:
        print(degree)
    print()

    # Decide based on the Euler theorem
    odd_count = 0
    for degree in g:
        if degree % 2 != 0:
            odd_count += 1

    if odd_count == 0 or odd_count == 2:
        if odd_count == 0:
            print("Each node has an even degree,")
            print("therefore, the graph has an Euler circuit.")
        else:
            print("The degree of exactly two nodes is odd,")
            print("therefore, the graph has an Euler path,")
            print("but no Euler circuit.")
    else:
        if odd_count == 1:
            print("Since", odd_count, "node has an odd degree,")
        else:
            print("Since", odd_count, "nodes have an odd degree,")
        print("the graph has neither an Euler circuit nor an Euler path.")

if __name__ == "__main__":
    print("Enter the number of nodes (maximum 20):")
    n = int(input())

    # Input the adjacency matrix
    a = []
    for i in range(n):
        row = []
        for j in range(n):
            print(f"a({i+1},{j+1}) = ", end="")
            row.append(int(input()))
        a.append(row)

    euler_path_cycle(n, a)