Problem: Find bridges of an undirected graph G(V, E).

A bridge (also known as a cut-edge) is an edge whose deletion increase the number of connected components.

Constraints

* 1 ≤ |V| ≤ 100,000
* 0 ≤ |E| ≤ 100,000
* The graph is connected
* There are no parallel edges
* There are no self-loops

Input


|V| |E|
s0 t0
s1 t1
:
s|E|-1 t|E|-1


, where |V| is the number of nodes and |E| is the number of edges in the graph. The graph nodes are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target nodes of i-th edge (undirected).

Output

A list of bridges of the graph ordered by name. For each bridge, names of its end-ponints, source and target (source < target), should be printed separated by a space. The sources should be printed ascending order, then the target should also be printed ascending order for the same source.

Examples

Input

4 4
0 1
0 2
1 2
2 3


Output

2 3


Input

5 4
0 1
1 2
2 3
3 4


Output

0 1
1 2
2 3
3 4

Solution (in PYTHON3):

Solution:
from math import inf
import sys
input = lambda: sys.stdin.readline().rstrip()
sys.setrecursionlimit(10**6)


def dfs(v,par):
    global cur
    vis[v]=1 ; disc[v]=cur ;low[v]=cur 
    cur+=1
    for i in g[v]:
        if vis[i]==0:
            dfs(i,v)
            low[v]=min(low[i],low[v])
            if low[i]>disc[v]:
                apts.add((min(v,i),max(v,i)))

        elif i!=par: low[v]=min(disc[i],low[v])
   
def articulation_pts():
    global apts,disc,low,vis
    disc=[0]*n ; low=[inf]*n ; vis=[0]*n ; apts=set()  
    for i in range(n):
        if vis[i]==0:
            dfs(i,-1)

n,e=map(int,input().split())
cur=0
g=[[] for i in range(n)]
for i in range(e):
    x,y=map(int,input().split())
    g[x].append(y)
    g[y].append(x)
articulation_pts()
apts=sorted(apts)
for i in apts:
    print(*i)