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:
# -*- coding: utf-8 -*-

import sys

sys.setrecursionlimit(10 ** 9)
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
INF=float('inf')

N,M=MAP()
nodes=[[] for i in range(N)]
for i in range(M):
    u,v=MAP()
    nodes[u].append(v)
    nodes[v].append(u)

visited=[False]*N
timer=1
prenum=[0]*(N+1)
lowest=[0]*(N+1)
ans=[]
def rec(cur, prev):
    global timer
    # curを訪問した直後の処理
    prenum[cur]=lowest[cur]=timer
    timer+=1

    visited[cur]=True
    for nxt in nodes[cur]:
        # 未訪問なら再帰探索する
        if not visited[nxt]:
            rec(nxt, cur)
            # nxtの探索が終了した直後の処理
            lowest[cur]=min(lowest[cur], lowest[nxt])
            # より近い経路を含まないなら橋とする
            if lowest[nxt]==prenum[nxt]:
                # 番号の小さい方から入れる
                ans.append((min(cur, nxt), max(cur, nxt)))
        # 訪問済の場合、親への経路は無視して、他は近い経路となるか確認を取る
        elif nxt!=prev:
            lowest[cur]=min(lowest[cur], lowest[nxt])

rec(0, -1)

ans.sort()
for edge in ans:
    print(*edge)