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:
import sys
sys.setrecursionlimit(10**6)

V, E = list(map(int, input().split()))
G = [[] for i in range(V)]

for i in range(E):
    s, t = list(map(int, input().split()))
    G[s].append(t)
    G[t].append(s)

class LowLink:
    def main(G, V):
        LowLink.G = G
        LowLink.used = [False] * V
        LowLink.ord = [0] * V
        LowLink.low = [0] * V
        LowLink.aps = []
        LowLink.bridges = []
        n = 0
        
        for i in range(V):
            if not LowLink.used[i]: n = LowLink.dfs(i, n, -1)
            
        LowLink.aps.sort()
        LowLink.bridges.sort()
        
    def dfs(v, n, par):
        LowLink.used[v] = True
        LowLink.ord[v] = n+1
        n += 1
        LowLink.low[v] = LowLink.ord[v]
        
        is_aps = False
        chi = 0
        
        for u in LowLink.G[v]:
            if not LowLink.used[u]:
                chi += 1
                n = LowLink.dfs(u, n, v)
                LowLink.low[v] = min(LowLink.low[v], LowLink.low[u])
                if par != -1 and LowLink.ord[v] <= LowLink.low[u]: is_aps = True
                if LowLink.ord[v] < LowLink.low[u]: LowLink.bridges.append((min(v, u), max(v, u)))
                
            elif u != par:
                LowLink.low[v] = min(LowLink.low[v], LowLink.ord[u])
                
        if par == -1 and chi >= 2: is_aps = True
        if is_aps: LowLink.aps.append(v)

        return n

LowLink.main(G, V)      

for v in LowLink.bridges:
    print(*v)