Buggy python submission (verdict: Time Limit Exceeded):
n,m=map(int, input().split())
ab=[list(map(int,input().split())) for i in range(m)]

from pprint import pprint

l=[[False for _ in range(n)] for _ in range(n)]
v=[True for _ in range(n)]
for a,b in ab:
    l[b-1][a-1], l[a-1][b-1]=True,True

def dfs(x,t,v,j,m,n):
    j+=1
    if j<=m:
        v[x]=False
        for i in range(1,n):
            if t[x][i]:
                dfs(i,t,v,j,m,n)
import copy

ans=0
for i in range(m):
    j=0
    t=copy.deepcopy(l)
    t[ab[i][1]-1][ab[i][0]-1],t[ab[i][0]-1][ab[i][1]-1]=False,False
    v=[True for _ in range(n)]
    if i!=0:
        dfs(ab[0][0]-1, t, v, j, m,n)
    else:
        dfs(ab[1][0]-1, t, v, j, m,n)
        
    z=False
    for x in v:
        if x:
            z=True
    if z:
        ans+=1
print(ans)

Fixed submission:
n,m=map(int, input().split())
ab=[list(map(int,input().split())) for i in range(m)]

from pprint import pprint

l=[[False for _ in range(n)] for _ in range(n)]
v=[True for _ in range(n)]
for a,b in ab:
    l[b-1][a-1], l[a-1][b-1]=True,True
def dfs(x,t,v,j,m,n):
    j+=1
    if j<n+m:
        v[x]=False
        for i in range(1,n):
            if v[i]:
                if t[x][i]:
                    dfs(i,t,v,j,m,n)
import copy

ans=0
for i in range(m):
    j=0
    t=copy.deepcopy(l)
    t[ab[i][1]-1][ab[i][0]-1],t[ab[i][0]-1][ab[i][1]-1]=False,False
    v=[True for _ in range(n)]
    dfs(0, t, v, j, m,n)
        
    z=False
    for x in v:
        if x:
            z=True
    if z:
        ans+=1
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
n,m=map(int, input().split())
ab=[list(map(int,input().split())) for i in range(m)]

from pprint import pprint

l=[[False for _ in range(n)] for _ in range(n)]
v=[True for _ in range(n)]
for a,b in ab:
    l[b-1][a-1], l[a-1][b-1]=True,True

def dfs(x,t,v,j,m,n):
    j+=1
    if j<n+m:
        v[x]=False
        for i in range(1,n):
            if t[x][i]:
                dfs(i,t,v,j,m,n)
import copy

ans=0
for i in range(m):
    j=0
    t=copy.deepcopy(l)
    t[ab[i][1]-1][ab[i][0]-1],t[ab[i][0]-1][ab[i][1]-1]=False,False
    v=[True for _ in range(n)]
    if i!=0:
        dfs(ab[0][0]-1, t, v, j, m,n)
    else:
        dfs(ab[1][0]-1, t, v, j, m,n)
        
    z=False
    for x in v:
        if x:
            z=True
    if z:
        ans+=1
print(ans)

Fixed submission:
n,m=map(int, input().split())
ab=[list(map(int,input().split())) for i in range(m)]

from pprint import pprint

l=[[False for _ in range(n)] for _ in range(n)]
v=[True for _ in range(n)]
for a,b in ab:
    l[b-1][a-1], l[a-1][b-1]=True,True
def dfs(x,t,v,j,m,n):
    j+=1
    if j<n+m:
        v[x]=False
        for i in range(1,n):
            if v[i]:
                if t[x][i]:
                    dfs(i,t,v,j,m,n)
import copy

ans=0
for i in range(m):
    j=0
    t=copy.deepcopy(l)
    t[ab[i][1]-1][ab[i][0]-1],t[ab[i][0]-1][ab[i][1]-1]=False,False
    v=[True for _ in range(n)]
    dfs(0, t, v, j, m,n)
        
    z=False
    for x in v:
        if x:
            z=True
    if z:
        ans+=1
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
n,m=map(int, input().split())
ab=[list(map(int,input().split())) for i in range(m)]

from pprint import pprint

l=[[False for _ in range(n)] for _ in range(n)]
v=[True for _ in range(n)]
for a,b in ab:
    l[b-1][a-1], l[a-1][b-1]=True,True

def dfs(x,t,v,j,m,n):
    j+=1
    if j<n+m:
        v[x]=False
        for i in range(1,n):
            if t[x][i]:
                dfs(i,t,v,j,m,n)

ans=0
for i in range(m):
    j=0
    t=[[False for _ in range(n)] for _ in range(n)]
    for a,b in ab:
        t[b-1][a-1],t[a-1][b-1]=True,True
    t[ab[i][1]-1][ab[i][0]-1],t[ab[i][0]-1][ab[i][1]-1]=False,False
    v=[True for _ in range(n)]
    if i!=0:
        dfs(ab[0][0]-1, t, v, j, m,n)
    else:
        dfs(ab[1][0]-1, t, v, j, m,n)
        
    z=False
    for x in v:
        if x:
            z=True
    if z:
        ans+=1
print(ans)


    

Fixed submission:
n,m=map(int, input().split())
ab=[list(map(int,input().split())) for i in range(m)]

from pprint import pprint

l=[[False for _ in range(n)] for _ in range(n)]
v=[True for _ in range(n)]
for a,b in ab:
    l[b-1][a-1], l[a-1][b-1]=True,True
def dfs(x,t,v,j,m,n):
    j+=1
    if j<n+m:
        v[x]=False
        for i in range(1,n):
            if v[i]:
                if t[x][i]:
                    dfs(i,t,v,j,m,n)
import copy

ans=0
for i in range(m):
    j=0
    t=copy.deepcopy(l)
    t[ab[i][1]-1][ab[i][0]-1],t[ab[i][0]-1][ab[i][1]-1]=False,False
    v=[True for _ in range(n)]
    dfs(0, t, v, j, m,n)
        
    z=False
    for x in v:
        if x:
            z=True
    if z:
        ans+=1
print(ans)