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from __future__ import print_function

try:

raw_input # Python 2

except NameError:

raw_input = input # Python 3

try:

xrange # Python 2

except NameError:

xrange = range # Python 3

# Accept No. of Nodes and edges

n, m = map(int, raw_input().split(" "))

# Initialising Dictionary of edges

g = {}

for i in xrange(n):

g[i + 1] = []

"""

--------------------------------------------------------------------------------

Accepting edges of Unweighted Directed Graphs

--------------------------------------------------------------------------------

"""

for _ in xrange(m):

x, y = map(int, raw_input().split(" "))

g[x].append(y)

"""

--------------------------------------------------------------------------------

Accepting edges of Unweighted Undirected Graphs

--------------------------------------------------------------------------------

"""

for _ in xrange(m):

x, y = map(int, raw_input().split(" "))

g[x].append(y)

g[y].append(x)

"""

--------------------------------------------------------------------------------

Accepting edges of Weighted Undirected Graphs

--------------------------------------------------------------------------------

"""

for _ in xrange(m):

x, y, r = map(int, raw_input().split(" "))

g[x].append([y, r])

g[y].append([x, r])

"""

--------------------------------------------------------------------------------

Depth First Search.

Args : G - Dictionary of edges

s - Starting Node

Vars : vis - Set of visited nodes

S - Traversal Stack

--------------------------------------------------------------------------------

"""

def dfs(G, s):

vis, S = set([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 - Traveral Stack

--------------------------------------------------------------------------------

"""

from collections import deque

def bfs(G, s):

vis, Q = set([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):

dist, known, path = {s: 0}, set(), {s: 0}

while True:

if len(known) == len(G) - 1:

break

mini = 100000

for i in dist:

if i not in known and dist[i] < mini:

mini = dist[i]

u = i

known.add(u)

for v in G[u]:

if v[0] not in known:

if dist[u] + v[1] < dist.get(v[0], 100000):

dist[v[0]] = dist[u] + v[1]

path[v[0]] = u

for i in dist:

if i != s:

print(dist[i])

"""

--------------------------------------------------------------------------------

Topological Sort

--------------------------------------------------------------------------------

"""

from collections import deque

def topo(G, ind=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():

n, a = raw_input(), []

for i in xrange(n):

a.append(map(int, raw_input().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 xrange(n)]

for k in xrange(n):

for i in xrange(n):

for j in xrange(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 i in dist:

if i not in known and dist[i] < mini:

mini = dist[i]

u = i

known.add(u)

for v in G[u]:

if v[0] not in known:

if v[1] < dist.get(v[0], 100000):

dist[v[0]] = v[1]

path[v[0]] = u

"""

--------------------------------------------------------------------------------

Accepting Edge list

Vars : n - Number of nodes

m - Number of edges

Returns : l - Edge list

n - Number of Nodes

--------------------------------------------------------------------------------

"""

def edglist():

n, m = map(int, raw_input().split(" "))

l = []

for i in xrange(m):

l.append(map(int, raw_input().split(' ')))

return l, 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 = [set([i]) for i in range(1, n + 1)]

while True:

if len(s) == 1:

break

print(s)

x = E.pop()

for i in xrange(len(s)):

if x[0] in s[i]:

break

for j in xrange(len(s)):

if x[1] in s[j]:

if i == j:

break

s[j].update(s[i])

s.pop(i)

break

# find the isolated node in the graph

def find_isolated_nodes(graph):

isolated = []

for node in graph:

if not graph[node]:

isolated.append(node)

return isolated

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