Buggy python submission (verdict: Time Limit Exceeded):
import unittest


class TestG(unittest.TestCase):
    def test_1(self):
        self.assertEqual(
            think(
                4,
                [
                  [1, 2], [1, 3], [3, 2],
                  [2, 4], [3, 4]
                ]
            ),
            3
        )

    def test_2(self):
        self.assertEqual(
            think(
                6,
                [
                    [2, 3], [4, 5], [5, 6]
                ]
            ),
            2
        )

    def test_3(self):
        self.assertEqual(
            think(
                5,
                [
                    [5, 3], [2, 3], [2, 4], [5, 2],
                    [5, 1], [1, 4], [4, 3], [1, 3]
                ]
            ),
            3
        )


def solve():
    n, list_of_x_and_y = read()
    result = think(n, list_of_x_and_y)
    write(result)


def read():
    n, m = read_int(2)
    list_of_x_and_y = []
    for _ in range(m):
        list_of_x_and_y.append(read_int(2))
    return n, list_of_x_and_y


def read_int(n):
    return read_type(int, n, sep=' ')


def read_float(n):
    return read_type(float, n, sep=' ')


def read_type(t, n, sep):
    return list(map(lambda x: t(x), read_line().split(sep)))[:n]


def read_line(n=0):
    if n == 0:
        return input().rstrip()
    else:
        return input().rstrip()[:n]


def think(n, list_of_x_and_y):
    inf = n ** 2
    adjacency_matrix = create_adjacency_matrix(n, list_of_x_and_y)
    max_distance = 0
    for i in range(n):
        max_distance = max(max_distance, scan_max_distance_from(n, i, [], adjacency_matrix))
    return max_distance


def write(result):
    print(result)


def create_adjacency_matrix(n, list_of_x_and_y):
    matrix = prepare_empty_matrix(n, 0)
    for x, y in list_of_x_and_y:
        matrix[x - 1][y - 1] = 1
    return matrix


def prepare_empty_matrix(n, initial_value):
    return [[initial_value for y in range(n)] for x in range(n)]


def scan_max_distance_from(n, at, path, adjacency_matrix):
    max_distance = len(path)
    for i in range(n):
        if i in path:
            continue
        if adjacency_matrix[at][i] == 0:
            continue
        path.append(i)
        max_distance = max(
            max_distance,
            scan_max_distance_from(n, i, path, adjacency_matrix)
        )
        path.remove(i)
    return max_distance


if __name__ == '__main__':
    import sys
    sys.setrecursionlimit(100000)
    # unittest.main()
    solve()

Fixed submission:
import sys

def solve():
    n, list_of_xy = read()
    result = think(n, list_of_xy)
    write(result)


def read():
    n, m = read_int(2)
    list_of_xy = []
    for i in range(m):
        list_of_xy.append(read_int(2))
    return n, list_of_xy


def read_int(n):
    return list(map(lambda x: int(x), read_line().split(' ')))[:n]


def read_line(n=0):
    if n == 0:
        return input().rstrip()
    else:
        return input().rstrip()[:n]


def think(n, list_of_xy):
    num_of_input_edges = [0 for _ in range(n + 1)]
    num_of_output_edges = [0 for _ in range(n + 1)]

    linked_list = generate_linked_list(list_of_xy)

    invalid_value = -1
    length_of_longest_path_start_from = [invalid_value for _ in range(n + 1)]

    for x, y in list_of_xy:
        num_of_input_edges[y] += 1
        num_of_output_edges[x] += 1

    for i in range(1, len(num_of_input_edges)):
        if num_of_output_edges[i] == 0:
            length_of_longest_path_start_from[i] = 0

    for i in range(1, len(num_of_input_edges)):
        if num_of_input_edges[i] == 0:
            update_logest_path_start_from(i, linked_list, length_of_longest_path_start_from, invalid_value)

    return max(length_of_longest_path_start_from)


def generate_linked_list(list_of_xy):
    linked_list = {}
    for x, y in list_of_xy:
        if x in linked_list:
            linked_list[x].append(y)
        else:
            linked_list[x] = [y]
    return linked_list


def update_logest_path_start_from(x, linked_list, length_of_longest_path_start_from, invalid_value):
    if length_of_longest_path_start_from[x] != invalid_value:
        return

    dest_from_x = linked_list.get(x, [])
    for y in dest_from_x:
        if length_of_longest_path_start_from[y] == invalid_value:
            update_logest_path_start_from(y, linked_list, length_of_longest_path_start_from, invalid_value)
            length_of_longest_path_start_from[x] = max(length_of_longest_path_start_from[x], length_of_longest_path_start_from[y] + 1)
        else:
            length_of_longest_path_start_from[x] = max(length_of_longest_path_start_from[x], length_of_longest_path_start_from[y] + 1)


def write(result):
    print(result)


if __name__ == '__main__':
    sys.setrecursionlimit(10 ** 5)
    solve()

Buggy python submission (verdict: Runtime Error):
def solve():
    n, list_of_xy = read()
    result = think(n, list_of_xy)
    write(result)


def read():
    n, m = read_int(2)
    list_of_xy = []
    for i in range(m):
        list_of_xy.append(read_int(2))
    return n, list_of_xy


def read_int(n):
    return list(map(lambda x: int(x), read_line().split(' ')))[:n]


def read_line(n=0):
    if n == 0:
        return input().rstrip()
    else:
        return input().rstrip()[:n]


def think(n, list_of_xy):
    num_of_input_edges = [0 for _ in range(n + 1)]
    num_of_output_edges = [0 for _ in range(n + 1)]

    linked_list = generate_linked_list(list_of_xy)

    invalid_value = -1
    length_of_longest_path_start_from = [invalid_value for _ in range(n + 1)]

    for x, y in list_of_xy:
        num_of_input_edges[y] += 1
        num_of_output_edges[x] += 1

    for i in range(1, len(num_of_input_edges)):
        if num_of_output_edges[i] == 0:
            length_of_longest_path_start_from[i] = 0

    for i in range(1, len(num_of_input_edges)):
        if num_of_input_edges[i] == 0:
            update_logest_path_start_from(i, linked_list, length_of_longest_path_start_from, invalid_value)

    return max(length_of_longest_path_start_from)


def generate_linked_list(list_of_xy):
    linked_list = {}
    for x, y in list_of_xy:
        if x in linked_list:
            linked_list[x].append(y)
        else:
            linked_list[x] = [y]
    return linked_list


def update_logest_path_start_from(x, linked_list, length_of_longest_path_start_from, invalid_value):
    if length_of_longest_path_start_from[x] != invalid_value:
        return

    dest_from_x = linked_list.get(x, [])
    for y in dest_from_x:
        if length_of_longest_path_start_from[y] == invalid_value:
            update_logest_path_start_from(y, linked_list, length_of_longest_path_start_from, invalid_value)
            length_of_longest_path_start_from[x] = max(length_of_longest_path_start_from[x], length_of_longest_path_start_from[y] + 1)
        else:
            length_of_longest_path_start_from[x] = max(length_of_longest_path_start_from[x], length_of_longest_path_start_from[y] + 1)


def write(result):
    print(result)


if __name__ == '__main__':
    solve()

Fixed submission:
import sys

def solve():
    n, list_of_xy = read()
    result = think(n, list_of_xy)
    write(result)


def read():
    n, m = read_int(2)
    list_of_xy = []
    for i in range(m):
        list_of_xy.append(read_int(2))
    return n, list_of_xy


def read_int(n):
    return list(map(lambda x: int(x), read_line().split(' ')))[:n]


def read_line(n=0):
    if n == 0:
        return input().rstrip()
    else:
        return input().rstrip()[:n]


def think(n, list_of_xy):
    num_of_input_edges = [0 for _ in range(n + 1)]
    num_of_output_edges = [0 for _ in range(n + 1)]

    linked_list = generate_linked_list(list_of_xy)

    invalid_value = -1
    length_of_longest_path_start_from = [invalid_value for _ in range(n + 1)]

    for x, y in list_of_xy:
        num_of_input_edges[y] += 1
        num_of_output_edges[x] += 1

    for i in range(1, len(num_of_input_edges)):
        if num_of_output_edges[i] == 0:
            length_of_longest_path_start_from[i] = 0

    for i in range(1, len(num_of_input_edges)):
        if num_of_input_edges[i] == 0:
            update_logest_path_start_from(i, linked_list, length_of_longest_path_start_from, invalid_value)

    return max(length_of_longest_path_start_from)


def generate_linked_list(list_of_xy):
    linked_list = {}
    for x, y in list_of_xy:
        if x in linked_list:
            linked_list[x].append(y)
        else:
            linked_list[x] = [y]
    return linked_list


def update_logest_path_start_from(x, linked_list, length_of_longest_path_start_from, invalid_value):
    if length_of_longest_path_start_from[x] != invalid_value:
        return

    dest_from_x = linked_list.get(x, [])
    for y in dest_from_x:
        if length_of_longest_path_start_from[y] == invalid_value:
            update_logest_path_start_from(y, linked_list, length_of_longest_path_start_from, invalid_value)
            length_of_longest_path_start_from[x] = max(length_of_longest_path_start_from[x], length_of_longest_path_start_from[y] + 1)
        else:
            length_of_longest_path_start_from[x] = max(length_of_longest_path_start_from[x], length_of_longest_path_start_from[y] + 1)


def write(result):
    print(result)


if __name__ == '__main__':
    sys.setrecursionlimit(10 ** 5)
    solve()

Buggy python submission (verdict: Runtime Error):
def solve():
    n, list_of_xy = read()
    result = think(n, list_of_xy)
    write(result)


def read():
    n, m = read_int(2)
    list_of_xy = []
    for i in range(m):
        list_of_xy.append(read_int(2))
    return n, list_of_xy


def read_int(n):
    return list(map(lambda x: int(x), read_line().split(' ')))[:n]


def read_line(n=0):
    if n == 0:
        return input().rstrip()
    else:
        return input().rstrip()[:n]


def think(n, list_of_xy):
    num_of_input_edges = [0 for _ in range(n + 1)]
    num_of_output_edges = [0 for _ in range(n + 1)]

    linked_list = generate_linked_list(list_of_xy)

    invalid_value = -1
    length_of_longest_path_start_from = [invalid_value for _ in range(n + 1)]

    for x, y in list_of_xy:
        num_of_input_edges[y] += 1
        num_of_output_edges[x] += 1

    for i in range(1, len(num_of_input_edges)):
        if num_of_output_edges[i] == 0:
            length_of_longest_path_start_from[i] = 0

    for i in range(1, len(num_of_input_edges)):
        if num_of_input_edges[i] == 0:
            update_logest_path_start_from(i, linked_list, length_of_longest_path_start_from, invalid_value)

    return max(length_of_longest_path_start_from)


def generate_linked_list(list_of_xy):
    linked_list = {}
    for x, y in list_of_xy:
        if x in linked_list:
            linked_list[x].append(y)
        else:
            linked_list[x] = [y]
    return linked_list


def update_logest_path_start_from(x, linked_list, length_of_longest_path_start_from, invalid_value):
    if length_of_longest_path_start_from[x] != invalid_value:
        return

    dest_from_x = linked_list[x]
    for y in dest_from_x:
        if length_of_longest_path_start_from[y] == invalid_value:
            update_logest_path_start_from(y, linked_list, length_of_longest_path_start_from, invalid_value)
            length_of_longest_path_start_from[x] = max(length_of_longest_path_start_from[x], length_of_longest_path_start_from[y] + 1)
        else:
            length_of_longest_path_start_from[x] = max(length_of_longest_path_start_from[x], length_of_longest_path_start_from[y] + 1)


def write(result):
    print(result)


if __name__ == '__main__':
    solve()

Fixed submission:
import sys

def solve():
    n, list_of_xy = read()
    result = think(n, list_of_xy)
    write(result)


def read():
    n, m = read_int(2)
    list_of_xy = []
    for i in range(m):
        list_of_xy.append(read_int(2))
    return n, list_of_xy


def read_int(n):
    return list(map(lambda x: int(x), read_line().split(' ')))[:n]


def read_line(n=0):
    if n == 0:
        return input().rstrip()
    else:
        return input().rstrip()[:n]


def think(n, list_of_xy):
    num_of_input_edges = [0 for _ in range(n + 1)]
    num_of_output_edges = [0 for _ in range(n + 1)]

    linked_list = generate_linked_list(list_of_xy)

    invalid_value = -1
    length_of_longest_path_start_from = [invalid_value for _ in range(n + 1)]

    for x, y in list_of_xy:
        num_of_input_edges[y] += 1
        num_of_output_edges[x] += 1

    for i in range(1, len(num_of_input_edges)):
        if num_of_output_edges[i] == 0:
            length_of_longest_path_start_from[i] = 0

    for i in range(1, len(num_of_input_edges)):
        if num_of_input_edges[i] == 0:
            update_logest_path_start_from(i, linked_list, length_of_longest_path_start_from, invalid_value)

    return max(length_of_longest_path_start_from)


def generate_linked_list(list_of_xy):
    linked_list = {}
    for x, y in list_of_xy:
        if x in linked_list:
            linked_list[x].append(y)
        else:
            linked_list[x] = [y]
    return linked_list


def update_logest_path_start_from(x, linked_list, length_of_longest_path_start_from, invalid_value):
    if length_of_longest_path_start_from[x] != invalid_value:
        return

    dest_from_x = linked_list.get(x, [])
    for y in dest_from_x:
        if length_of_longest_path_start_from[y] == invalid_value:
            update_logest_path_start_from(y, linked_list, length_of_longest_path_start_from, invalid_value)
            length_of_longest_path_start_from[x] = max(length_of_longest_path_start_from[x], length_of_longest_path_start_from[y] + 1)
        else:
            length_of_longest_path_start_from[x] = max(length_of_longest_path_start_from[x], length_of_longest_path_start_from[y] + 1)


def write(result):
    print(result)


if __name__ == '__main__':
    sys.setrecursionlimit(10 ** 5)
    solve()

Buggy python submission (verdict: Time Limit Exceeded):
def solve():
    n, list_of_xy = read()
    result = think(n, list_of_xy)
    write(result)


def read():
    n, m = read_int(2)
    list_of_xy = []
    for i in range(m):
        list_of_xy.append(read_int(2))
    return n, list_of_xy


def read_int(n):
    return list(map(lambda x: int(x), read_line().split(' ')))[:n]


def read_line(n=0):
    if n == 0:
        return input().rstrip()
    else:
        return input().rstrip()[:n]


def think(n, list_of_xy):
    num_of_input_edges = [0 for _ in range(n + 1)]
    num_of_output_edges = [0 for _ in range(n + 1)]

    invalid_value = -1
    length_of_longest_path_start_from = [invalid_value for _ in range(n + 1)]

    for x, y in list_of_xy:
        num_of_input_edges[y] += 1
        num_of_output_edges[x] += 1

    for i in range(1, len(num_of_input_edges)):
        if num_of_output_edges[i] == 0:
            length_of_longest_path_start_from[i] = 0

    for i in range(1, len(num_of_input_edges)):
        if num_of_input_edges[i] == 0:
            update_logest_path_start_from(i, list_of_xy, length_of_longest_path_start_from, invalid_value)

    return max(length_of_longest_path_start_from)


def update_logest_path_start_from(start_from, list_of_xy, length_of_longest_path_start_from, invalid_value):
    if length_of_longest_path_start_from[start_from] != invalid_value:
        return

    subset_of_list_of_xy = list(filter(lambda x: x[0] == start_from, list_of_xy))
    for x, y in subset_of_list_of_xy:
        if length_of_longest_path_start_from[y] == invalid_value:
            update_logest_path_start_from(y, list_of_xy, length_of_longest_path_start_from, invalid_value)
            length_of_longest_path_start_from[x] = max(length_of_longest_path_start_from[x], length_of_longest_path_start_from[y] + 1)
        else:
            length_of_longest_path_start_from[x] = max(length_of_longest_path_start_from[x], length_of_longest_path_start_from[y] + 1)


def write(result):
    print(result)


if __name__ == '__main__':
    solve()

Fixed submission:
import sys

def solve():
    n, list_of_xy = read()
    result = think(n, list_of_xy)
    write(result)


def read():
    n, m = read_int(2)
    list_of_xy = []
    for i in range(m):
        list_of_xy.append(read_int(2))
    return n, list_of_xy


def read_int(n):
    return list(map(lambda x: int(x), read_line().split(' ')))[:n]


def read_line(n=0):
    if n == 0:
        return input().rstrip()
    else:
        return input().rstrip()[:n]


def think(n, list_of_xy):
    num_of_input_edges = [0 for _ in range(n + 1)]
    num_of_output_edges = [0 for _ in range(n + 1)]

    linked_list = generate_linked_list(list_of_xy)

    invalid_value = -1
    length_of_longest_path_start_from = [invalid_value for _ in range(n + 1)]

    for x, y in list_of_xy:
        num_of_input_edges[y] += 1
        num_of_output_edges[x] += 1

    for i in range(1, len(num_of_input_edges)):
        if num_of_output_edges[i] == 0:
            length_of_longest_path_start_from[i] = 0

    for i in range(1, len(num_of_input_edges)):
        if num_of_input_edges[i] == 0:
            update_logest_path_start_from(i, linked_list, length_of_longest_path_start_from, invalid_value)

    return max(length_of_longest_path_start_from)


def generate_linked_list(list_of_xy):
    linked_list = {}
    for x, y in list_of_xy:
        if x in linked_list:
            linked_list[x].append(y)
        else:
            linked_list[x] = [y]
    return linked_list


def update_logest_path_start_from(x, linked_list, length_of_longest_path_start_from, invalid_value):
    if length_of_longest_path_start_from[x] != invalid_value:
        return

    dest_from_x = linked_list.get(x, [])
    for y in dest_from_x:
        if length_of_longest_path_start_from[y] == invalid_value:
            update_logest_path_start_from(y, linked_list, length_of_longest_path_start_from, invalid_value)
            length_of_longest_path_start_from[x] = max(length_of_longest_path_start_from[x], length_of_longest_path_start_from[y] + 1)
        else:
            length_of_longest_path_start_from[x] = max(length_of_longest_path_start_from[x], length_of_longest_path_start_from[y] + 1)


def write(result):
    print(result)


if __name__ == '__main__':
    sys.setrecursionlimit(10 ** 5)
    solve()