from collections import deque


def _input(message):
 return input(message).strip().split(" ")


def initialize_unweighted_directed_graph(
 node_count: int, edge_count: int
) -> dict[int, list[int]]:
 graph: dict[int, list[int]] = {}
 for i in range(node_count):
 graph[i + 1] = []

 for e in range(edge_count):
 x, y = (int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> "))
 graph[x].append(y)
 return graph


def initialize_unweighted_undirected_graph(
 node_count: int, edge_count: int
) -> dict[int, list[int]]:
 graph: dict[int, list[int]] = {}
 for i in range(node_count):
 graph[i + 1] = []

 for e in range(edge_count):
 x, y = (int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> "))
 graph[x].append(y)
 graph[y].append(x)
 return graph


def initialize_weighted_undirected_graph(
 node_count: int, edge_count: int
) -> dict[int, list[tuple[int, int]]]:
 graph: dict[int, list[tuple[int, int]]] = {}
 for i in range(node_count):
 graph[i + 1] = []

 for e in range(edge_count):
 x, y, w = (int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> <weight> "))
 graph[x].append((y, w))
 graph[y].append((x, w))
 return graph


if __name__ == "__main__":
 n, m = (int(i) for i in _input("Number of nodes and edges: "))

 graph_choice = int(
 _input(
 "Press 1 or 2 or 3 \n"
 "1. Unweighted directed \n"
 "2. Unweighted undirected \n"
 "3. Weighted undirected \n"
 )[0]
 )

 g = {
 1: initialize_unweighted_directed_graph,
 2: initialize_unweighted_undirected_graph,
 3: initialize_weighted_undirected_graph,
 }[graph_choice](n, m)


"""
--------------------------------------------------------------------------------
 Depth First Search.
 Args : G - Dictionary of edges
 s - Starting Node
 Vars : vis - Set of visited nodes
 S - Traversal Stack
--------------------------------------------------------------------------------
"""


def dfs(g, s):
 """
 >>> dfs({1: [2, 3], 2: [4, 5], 3: [], 4: [], 5: []}, 1)
 1
 2
 4
 5
 3
 """
 vis, _s = {s}, [s]
 print(s)
 while _s:
 flag = 0
 for i in g[_s[-1]]:
 if i not in vis:
 _s.append(i)
 vis.add(i)
 flag = 1
 print(i)
 break
 if not flag:
 _s.pop()


"""
--------------------------------------------------------------------------------
 Breadth First Search.
 Args : G - Dictionary of edges
 s - Starting Node
 Vars : vis - Set of visited nodes
 Q - Traversal Stack
--------------------------------------------------------------------------------
"""


def bfs(g, s):
 """
 >>> bfs({1: [2, 3], 2: [4, 5], 3: [6, 7], 4: [], 5: [8], 6: [], 7: [], 8: []}, 1)
 1
 2
 3
 4
 5
 6
 7
 8
 """
 vis, q = {s}, deque([s])
 print(s)
 while q:
 u = q.popleft()
 for v in g[u]:
 if v not in vis:
 vis.add(v)
 q.append(v)
 print(v)


"""
--------------------------------------------------------------------------------
 Dijkstra's shortest path Algorithm
 Args : G - Dictionary of edges
 s - Starting Node
 Vars : dist - Dictionary storing shortest distance from s to every other node
 known - Set of knows nodes
 path - Preceding node in path
--------------------------------------------------------------------------------
"""


def dijk(g, s):
 """
 dijk({1: [(2, 7), (3, 9), (6, 14)],
 2: [(1, 7), (3, 10), (4, 15)],
 3: [(1, 9), (2, 10), (4, 11), (6, 2)],
 4: [(2, 15), (3, 11), (5, 6)],
 5: [(4, 6), (6, 9)],
 6: [(1, 14), (3, 2), (5, 9)]}, 1)
 7
 9
 11
 20
 20
 """
 dist, known, path = {s: 0}, set(), {s: 0}
 while True:
 if len(known) == len(g) - 1:
 break
 mini = 100000
 for key, value in dist:
 if key not in known and value < mini:
 mini = value
 u = key
 known.add(u)
 for v in g[u]:
 if v[0] not in known and dist[u] + v[1] < dist.get(v[0], 100000):
 dist[v[0]] = dist[u] + v[1]
 path[v[0]] = u
 for key, value in dist.items():
 if key != s:
 print(value)


"""
--------------------------------------------------------------------------------
 Topological Sort
--------------------------------------------------------------------------------
"""


def topo(g, ind=None, q=None):
 if q is None:
 q = [1]
 if ind is None:
 ind = [0] * (len(g) + 1) # SInce oth Index is ignored
 for u in g:
 for v in g[u]:
 ind[v] += 1
 q = deque()
 for i in g:
 if ind[i] == 0:
 q.append(i)
 if len(q) == 0:
 return
 v = q.popleft()
 print(v)
 for w in g[v]:
 ind[w] -= 1
 if ind[w] == 0:
 q.append(w)
 topo(g, ind, q)


"""
--------------------------------------------------------------------------------
 Reading an Adjacency matrix
--------------------------------------------------------------------------------
"""


def adjm():
 r"""
 Reading an Adjacency matrix

 Parameters:
 None

 Returns:
 tuple: A tuple containing a list of edges and number of edges

 Example:
 >>> # Simulate user input for 3 nodes
 >>> input_data = "4\n0 1 0 1\n1 0 1 0\n0 1 0 1\n1 0 1 0\n"
 >>> import sys,io
 >>> original_input = sys.stdin
 >>> sys.stdin = io.StringIO(input_data) # Redirect stdin for testing
 >>> adjm()
 ([(0, 1, 0, 1), (1, 0, 1, 0), (0, 1, 0, 1), (1, 0, 1, 0)], 4)
 >>> sys.stdin = original_input # Restore original stdin
 """
 n = int(input().strip())
 a = []
 for _ in range(n):
 a.append(tuple(map(int, input().strip().split())))
 return a, n


"""
--------------------------------------------------------------------------------
 Floyd Warshall's algorithm
 Args : G - Dictionary of edges
 s - Starting Node
 Vars : dist - Dictionary storing shortest distance from s to every other node
 known - Set of knows nodes
 path - Preceding node in path

--------------------------------------------------------------------------------
"""


def floy(a_and_n):
 (a, n) = a_and_n
 dist = list(a)
 path = [[0] * n for i in range(n)]
 for k in range(n):
 for i in range(n):
 for j in range(n):
 if dist[i][j] > dist[i][k] + dist[k][j]:
 dist[i][j] = dist[i][k] + dist[k][j]
 path[i][k] = k
 print(dist)


"""
--------------------------------------------------------------------------------
 Prim's MST Algorithm
 Args : G - Dictionary of edges
 s - Starting Node
 Vars : dist - Dictionary storing shortest distance from s to nearest node
 known - Set of knows nodes
 path - Preceding node in path
--------------------------------------------------------------------------------
"""


def prim(g, s):
 dist, known, path = {s: 0}, set(), {s: 0}
 while True:
 if len(known) == len(g) - 1:
 break
 mini = 100000
 for key, value in dist.items():
 if key not in known and value < mini:
 mini = value
 u = key
 known.add(u)
 for v in g[u]:
 if v[0] not in known and v[1] < dist.get(v[0], 100000):
 dist[v[0]] = v[1]
 path[v[0]] = u
 return dist


"""
--------------------------------------------------------------------------------
 Accepting Edge list
 Vars : n - Number of nodes
 m - Number of edges
 Returns : l - Edge list
 n - Number of Nodes
--------------------------------------------------------------------------------
"""


def edglist():
 r"""
 Get the edges and number of edges from the user

 Parameters:
 None

 Returns:
 tuple: A tuple containing a list of edges and number of edges

 Example:
 >>> # Simulate user input for 3 edges and 4 vertices: (1, 2), (2, 3), (3, 4)
 >>> input_data = "4 3\n1 2\n2 3\n3 4\n"
 >>> import sys,io
 >>> original_input = sys.stdin
 >>> sys.stdin = io.StringIO(input_data) # Redirect stdin for testing
 >>> edglist()
 ([(1, 2), (2, 3), (3, 4)], 4)
 >>> sys.stdin = original_input # Restore original stdin
 """
 n, m = tuple(map(int, input().split(" ")))
 edges = []
 for _ in range(m):
 edges.append(tuple(map(int, input().split(" "))))
 return edges, n


"""
--------------------------------------------------------------------------------
 Kruskal's MST Algorithm
 Args : E - Edge list
 n - Number of Nodes
 Vars : s - Set of all nodes as unique disjoint sets (initially)
--------------------------------------------------------------------------------
"""


def krusk(e_and_n):
 """
 Sort edges on the basis of distance
 """
 (e, n) = e_and_n
 e.sort(reverse=True, key=lambda x: x[2])
 s = [{i} for i in range(1, n + 1)]
 while True:
 if len(s) == 1:
 break
 print(s)
 x = e.pop()
 for i in range(len(s)):
 if x[0] in s[i]:
 break
 for j in range(len(s)):
 if x[1] in s[j]:
 if i == j:
 break
 s[j].update(s[i])
 s.pop(i)
 break


def find_isolated_nodes(graph):
 """
 Find the isolated node in the graph

 Parameters:
 graph (dict): A dictionary representing a graph.

 Returns:
 list: A list of isolated nodes.

 Examples:
 >>> graph1 = {1: [2, 3], 2: [1, 3], 3: [1, 2], 4: []}
 >>> find_isolated_nodes(graph1)
 [4]

 >>> graph2 = {'A': ['B', 'C'], 'B': ['A'], 'C': ['A'], 'D': []}
 >>> find_isolated_nodes(graph2)
 ['D']

 >>> graph3 = {'X': [], 'Y': [], 'Z': []}
 >>> find_isolated_nodes(graph3)
 ['X', 'Y', 'Z']

 >>> graph4 = {1: [2, 3], 2: [1, 3], 3: [1, 2]}
 >>> find_isolated_nodes(graph4)
 []

 >>> graph5 = {}
 >>> find_isolated_nodes(graph5)
 []
 """
 isolated = []
 for node in graph:
 if not graph[node]:
 isolated.append(node)
 return isolated