45_H. Road Problem
The Berland capital (as you very well know) contains n junctions, some pairs of which are connected by two-way roads. Unfortunately, the number of traffic jams in the capital has increased dramatically, that's why it was decided to build several new roads. Every road should connect two junctions. 

The city administration noticed that in the cities of all the developed countries between any two roads one can drive along at least two paths so that the paths don't share any roads (but they may share the same junction). The administration decided to add the minimal number of roads so that this rules was fulfilled in the Berland capital as well. In the city road network should exist no more than one road between every pair of junctions before or after the reform.

Input

The first input line contains a pair of integers n, m (2 ≤ n ≤ 900, 1 ≤ m ≤ 100000), where n is the number of junctions and m is the number of roads. Each of the following m lines contains a description of a road that is given by the numbers of the connected junctions ai, bi (1 ≤ ai, bi ≤ n, ai ≠ bi). The junctions are numbered from 1 to n. It is possible to reach any junction of the city from any other one moving along roads.

Output

On the first line print t — the number of added roads. Then on t lines print the descriptions of the added roads in the format of the input data. You can use any order of printing the roads themselves as well as the junctions linked by every road. If there are several solutions to that problem, print any of them.

If the capital doesn't need the reform, print the single number 0.

If there's no solution, print the single number -1.

Examples

Input

4 3
1 2
2 3
3 4


Output

1
1 4


Input

4 4
1 2
2 3
2 4
3 4


Output

1
1 3
```python
import sys
import threading

def main():

    
    p = input().split()
    n = int(p[0]) #number of locations
    m = int(p[1]) #number of passages

    if n==1: #if there's only one location, there's nothing to do
        print(0)
        return
    if n==2: #if there's only two nodes, the only edge between them, is always a bridge
        print(-1)
        return

    g = graph(n,m)

    g.buildBridgeTree()
    
    e = graph(len(g.bridges)+1,len(g.bridges))

    e.conexions= []
    e.pi=[]
    e.discovery=[]
    e.seen=[]

    for i in range(len(g.bridges)+1):
        e.conexions.append([])
        e.pi.append(-1)
        e.discovery.append(sys.float_info.max)
        e.seen.append(False)
    for i in range(len(g.bridges)):
        e.conexions[g.cc[g.bridges[i][0]]].append((g.cc[g.bridges[i][1]],True))
        e.conexions[g.cc[g.bridges[i][1]]].append((g.cc[g.bridges[i][0]],True))
    
    e.bridges=g.bridges
    e.bridge=g.bridge
    e.cc=g.cc
    e.CC=e.CC
    e.CC

    e.treeDiameter()

    print(len(e.newEdges))
    for i in range(len(e.newEdges)):
        u = e.newEdges[i][0] +1
        v = e.newEdges[i][1] +1
        print(u, end=" ")
        print(v)

class graph:

    n = int() #number of nodes
    edges= int() #number of edges
    time = int() 


    conexions = [] #adjacency list
    bridges=[] #are we using a removable edge or not for city i?
    bridge=[]


    discovery = [] #time to discover node i
    seen = [] #visited or not
    cc = [] #index of connected components
    low = [] #low[i]=min(discovery(i),discovery(w)) w:any node discoverable from i
    pi = [] #index of i's father 

    CC = []
    newEdges = []

    def __init__(self, n, m):

        self.n = n
        self.edges = m

        for i in range(self.n):
            self.conexions.append([])
            self.discovery.append(sys.float_info.max)
            self.low.append(sys.float_info.max)
            self.seen.append(False)
            self.cc.append(-1)
            self.CC.append([])
            self.bridge.append([])
            
    
    def buildGraph(self):
        #this method put every edge in the adjacency list
        for i in range(self.edges):
            p2=input().split()
            self.conexions[int(p2[0])-1].append((int(p2[1])-1,False))
            self.conexions[int(p2[1])-1].append((int(p2[0])-1,False))
    
    def searchBridges (self):
        self.time = 0 

        for i in range(self.n):
            self.pi.append(-1)
            for j in range(self.n):
                self.bridge[i].append(False)
        
        


        self.searchBridges_(0,-1) #we can start in any node 'cause the graph is connected

    
    def searchBridges_(self,c,index):

        self.seen[c]=True #mark as visited
        self.time+=1
        self.discovery[c]=self.low[c]= self.time

        for i in range(len(self.conexions[c])):
        
            pos = self.conexions[c][i][0]
            if not self.seen[pos]:
                self.pi[pos]=c #the node that discovered it
            
                self.searchBridges_(pos,i) #search throw its not visited conexions
            
                self.low[c]= min([self.low[c],self.low[pos]]) #definition of low
            
            elif self.pi[c]!=pos: #It is not the node that discovered it
                self.low[c]= min([self.low[c],self.discovery[pos]])
        
        if self.pi[c]!=-1 and self.low[c]==self.discovery[c]:  #it isn't the root and none of its connections is reacheable earlier than it
            self.bridges.append((c,self.pi[c]))
            self.bridge[self.pi[c]][c]=self.bridge[c][self.pi[c]]= True
            
            for i in range(len(self.conexions[c])):
                if(self.conexions[c][i][0]==self.pi[c]):
                    self.conexions[c][i]=(self.pi[c],True)
                    self.conexions[self.pi[c]][index]=(c,True)

        
            
        


    def findCC(self):

        j = 0

        for i in range(self.n):
            self.pi[i]=-1
            self.seen[i]=False
        
        for i in range(self.n):
            if self.seen[i]==False:
                self.cc[i]=j #assign the index of the new connected component
                self.CC[j].append(i)
                self.findCC_(i,j) #search throw its not visited conexions
                j+=1 #we finished the search in the connected component
    
    def findCC_(self, c, j):

        self.seen[c]=True #mark as visited

        for i in range(len(self.conexions[c])):

            pos = self.conexions[c][i][0]
            if(self.seen[pos]==False and self.conexions[c][i][1]==False):
                
                self.cc[pos]=j #assign the index of the connected component
                self.CC[j].append(pos)
                self.pi[pos]=c #the node that discovered it
                self.findCC_(pos,j) #search throw its not visited conexions

    def treeDiameter(self):

       while self.n>1:

            for i in range(self.n):
                self.seen[i]=False
                self.pi[i]=-1
            self.discovery[0]=0
            self.treeDiameter_(0) #search the distance from this node, to the others
            max = -1
            maxIndex = 0
            for i in range(self.n):
                if self.discovery[i]>max:
                    max= self.discovery[i] #look for the furthest node
                    maxIndex=i
            for i in range(self.n):
                self.seen[i]=False
                self.pi[i]=-1
            self.discovery[maxIndex]=0
            self.treeDiameter_(maxIndex)  #search the distance from the furthest node, to the others
            max =-1
            maxIndex2=-1
            for i in range(self.n):
                if self.discovery[i]>max :
                    max= self.discovery[i] #look for the furthest node to preview furthest node, and that is the diameter in a tree
                    maxIndex2=i
        
            self.ReBuildTree(maxIndex,maxIndex2)


    def treeDiameter_(self, c):

        self.seen[c]=True #mark as visited

        for i in range(len(self.conexions[c])):

            pos = self.conexions[c][i][0]

            if self.seen[pos]==False:

                self.pi[pos]=c #the node that discovered it
                self.discovery[pos]= self.discovery[c]+1 #distance to the node who discover it + 1
                #we don't have to compare and search for other paths, since it's a tree and there is only one path between two nodes.
                self.treeDiameter_(pos) #search throw its not visited conex16 ions



    def buildBridgeTree(self):
        
        self.buildGraph()
        self.searchBridges()
        self.findCC()

    def ReBuildTree(self, u, v):
        find=0

        for i in range(len(self.CC[u])):
            for j in range(len(self.CC[v])):
                if not self.bridge[self.CC[u][i]][self.CC[v][j]]:
                    self.newEdges.append((self.CC[u][i],self.CC[v][j]))
                    find=1
                    break
            
            if find==1:
                break

        newIndex=[]
        temp = v
        self.conexions[u]=None
        self.conexions[v]=None

        while self.pi[temp]!=u:
            self.conexions[self.pi[temp]]=None
            temp = self.pi[temp]

        r =1
        for i in range(self.n):
            if(self.conexions[i]!=None):
                newIndex.append(r)
                r+=1
            else:
                newIndex.append(0)
        
        self.n=r

        if self.n==1:
            return

        newCC=[]

        self.conexions=[]

        for i in range(self.n):
            self.conexions.append([])
            newCC.append([])

        for i in range(len(self.bridges)):

            len0 = len(self.CC[self.cc[self.bridges[i][0]]])
            

            if(len0!=0):
                for j in range(len0):
                    newCC[newIndex[self.cc[self.bridges[i][0]]]].append(self.CC[self.cc[self.bridges[i][0]]][j])
                self.CC[self.cc[self.bridges[i][0]]]=[]
            
            len1 = len(self.CC[self.cc[self.bridges[i][1]]])
            
            if(len1!=0):
                for j in range(len1):
                    newCC[newIndex[self.cc[self.bridges[i][1]]]].append(self.CC[self.cc[self.bridges[i][1]]][j])
                self.CC[self.cc[self.bridges[i][1]]]=[]
            
            self.conexions[newIndex[self.cc[self.bridges[i][0]]]].append((newIndex[self.cc[self.bridges[i][1]]],True))
            self.conexions[newIndex[self.cc[self.bridges[i][1]]]].append((newIndex[self.cc[self.bridges[i][0]]],True))

        self.CC= newCC

        for i in range(len(self.cc)):
            self.cc[i]=newIndex[self.cc[i]]





            





if __name__ == '__main__':
    main()
```