Buggy python submission (verdict: Runtime Error):
from bisect import *
from collections import *
from fractions import gcd
from math import factorial
from itertools import *
from heapq import *



N=int(input())
LR=[list(map(int,input().split())) for i in range(N)]
for i in range(N):
    LR[i][1]+=1

value=max([R-L for L,R in LR])
#LR=sorted(LR,key=lambda x:x[1])
LR=sorted(LR,key=lambda x:x[0]*10**9+x[1])
a=2*(10**9)
minRlst=[a for i in range(N)]
minRlst[-1]=LR[-1][1]
maxLlst=[0 for i in range(N)]
maxLlst[0]=LR[0][0]
for i in range(N-2,-1,-1):
    minRlst[i]=min(minRlst[i+1],LR[i][1])
for i in range(1,N):
    maxLlst[i]=max(minRlst[i-1],LR[i][0])
L1,R1=LR[0]
L2,R2=LR[-1][0],minRlst[1]
maxR=from bisect import *
from collections import *
from fractions import gcd
from math import factorial
from itertools import *
from heapq import *



N=int(input())
LR=[list(map(int,input().split())) for i in range(N)]
for i in range(N):
    LR[i][1]+=1

value=max([R-L for L,R in LR])
#LR=sorted(LR,key=lambda x:x[1])
LR=sorted(LR,key=lambda x:x[0]*10**9+x[1])
a=2*(10**9)
minRlst=[a for i in range(N)]
minRlst[-1]=LR[-1][1]
maxLlst=[0 for i in range(N)]
maxLlst[0]=LR[0][0]
for i in range(N-2,-1,-1):
    minRlst[i]=min(minRlst[i+1],LR[i][1])
for i in range(1,N):
    maxLlst[i]=min(minRlst[i-1],LR[i][0])
L1,R1=LR[0]
L2,R2=LR[-1][0],minRlst[1]
minR=min([R for L,R in LR])
for i in range(0,N-1):
    L,R=LR[i]
    a=max(R-L,0)
    b=max(minR-LR[-1][0],0)
    value=max(value,a+b)
    L1=L
    R1=min(R1,R)
    R2=minRlst[i+1]
    a=max(R1-L1,0)
    b=max(R2-L2,0)
    value=max(value,a+b)
print(value)
([R for L,R in LR])
for i in range(0,N-1):
    L,R=LR[i]
    a=max(R-L,0)
    b=max(maxR-LR[-1][0],0)
    value=max(value,a+b)
    L1=L
    R1=min(R1,R)
    R2=minRlst[i+1]
    a=max(R1-L1,0)
    b=max(R2-L2,0)
    value=max(value,a+b)
print(value)


Fixed submission:
from bisect import *
from collections import *
from fractions import gcd
from math import factorial
from itertools import *
from heapq import *



N=int(input())
LR=[list(map(int,input().split())) for i in range(N)]
for i in range(N):
    LR[i][1]+=1

value=max([R-L for L,R in LR])
#LR=sorted(LR,key=lambda x:x[1])
LR=sorted(LR,key=lambda x:x[0]*10**9+x[1])
a=2*(10**9)
minRlst=[a for i in range(N)]
minRlst[-1]=LR[-1][1]
maxLlst=[0 for i in range(N)]
maxLlst[0]=LR[0][0]
for i in range(N-2,-1,-1):
    minRlst[i]=min(minRlst[i+1],LR[i][1])
for i in range(1,N):
    maxLlst[i]=max(minRlst[i-1],LR[i][0])
L1,R1=LR[0]
L2,R2=LR[-1][0],minRlst[1]
maxR=min([R for L,R in LR])
for i in range(0,N-1):
    L,R=LR[i]
    a=max(R-L,0)
    b=max(maxR-LR[-1][0],0)
    value=max(value,a+b)
    L1=L
    R1=min(R1,R)
    R2=minRlst[i+1]
    a=max(R1-L1,0)
    b=max(R2-L2,0)
    value=max(value,a+b)
print(value)

Buggy python submission (verdict: Runtime Error):
from bisect import *
from collections import *
from fractions import gcd
from math import factorial
from itertools import *
from heapq import *
import math



N=int(input())
LR=[list(map(int,input().split())) for i in range(N)]
value=max([R-L for L,R in LR])+1
LR=sorted(LR,key=lambda x:x[0])

L1,R1=LR[0]
L2,R2=LR[1]
for i in range(2,N):
    L,R=LR[i]
    L2=L
    R2=min(R2,R)
a=max(R1-L1+1,0)
b=max(R2-L2+1,0)
value=max(value,a+b)

logN=math.log2(N)
#table=[[0 for i in range(logN)] for n in range(N)]
minRlst=[2*(10**10) for i in range(N)]
minRlst[-1]=LR[-1][1]
for i in range(N-2,-1,-1):
    minRlst[i]=min(minRlst[i+1],LR[i][1])
for i in range(1,N-1):
    L,R=LR[i]
    L1,R1=L,min(R1,R)
    R2=minRlst[i+1]
    a=max(R1+1-L1,0)
    b=max(R2+1-L2,0)
    value=max(value,a+b)
print(value)


Fixed submission:
from bisect import *
from collections import *
from fractions import gcd
from math import factorial
from itertools import *
from heapq import *



N=int(input())
LR=[list(map(int,input().split())) for i in range(N)]
for i in range(N):
    LR[i][1]+=1

value=max([R-L for L,R in LR])
#LR=sorted(LR,key=lambda x:x[1])
LR=sorted(LR,key=lambda x:x[0]*10**9+x[1])
a=2*(10**9)
minRlst=[a for i in range(N)]
minRlst[-1]=LR[-1][1]
maxLlst=[0 for i in range(N)]
maxLlst[0]=LR[0][0]
for i in range(N-2,-1,-1):
    minRlst[i]=min(minRlst[i+1],LR[i][1])
for i in range(1,N):
    maxLlst[i]=max(minRlst[i-1],LR[i][0])
L1,R1=LR[0]
L2,R2=LR[-1][0],minRlst[1]
maxR=min([R for L,R in LR])
for i in range(0,N-1):
    L,R=LR[i]
    a=max(R-L,0)
    b=max(maxR-LR[-1][0],0)
    value=max(value,a+b)
    L1=L
    R1=min(R1,R)
    R2=minRlst[i+1]
    a=max(R1-L1,0)
    b=max(R2-L2,0)
    value=max(value,a+b)
print(value)