Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np

n = int(input())
l = []
r = []
for i in range(n):
    li, ri = map(int, input().split())
    l.append(li)
    r.append(ri+1)

arglmax = l.index(max(l))
argrmin = r.index(min(r))
num = 0
for i in range(n):
    num = max(r[i] - l[i], num)
ans1 = num + max(0, r[argrmin]-l[arglmax])

lst = [l, r]
lst = list(np.array(lst).T)
lst = sorted(lst, key=lambda x: (x[0]), reverse=True)
lst = sorted(lst, key=lambda x: (x[1]))
lst = list(np.array(lst).T)
sorted_l = list(lst[0])
sorted_r = list(lst[1])

sorted_r_minus_lmax = list(np.array(sorted_r)-l[arglmax])
mini = sorted_r_minus_lmax[n-1]
for i in range(1, n):
    mini = min(mini, sorted_r_minus_lmax[n-1-i])
    sorted_r_minus_lmax[n-1-i] = mini

ans2 = 0
for i in range(n-1):
    ai = max(0, sorted_r_minus_lmax[i+1])
    bi = max(0, min(r[argrmin]-np.array(sorted_l[:i+1])))
    ans2 = max(ans2, ai+bi)

print(max(ans1, ans2))

Fixed submission:
import numpy as np

n = int(input())
l = []
r = []
for i in range(n):
    li, ri = map(int, input().split())
    l.append(li)
    r.append(ri+1)

arglmax = l.index(max(l))
argrmin = r.index(min(r))
num = 0
for i in range(n):
    num = max(r[i] - l[i], num)
ans1 = num + max(0, r[argrmin]-l[arglmax])

lst = [l, r]
lst = list(np.array(lst).T)
lst = sorted(lst, key=lambda x: (x[0]), reverse=True)
lst = sorted(lst, key=lambda x: (x[1]))
lst = list(np.array(lst).T)
sorted_l = list(lst[0])
sorted_r = list(lst[1])

sorted_r_minus_lmax = list(np.array(sorted_r)-l[arglmax])
mini = sorted_r_minus_lmax[n-1]
for i in range(1, n):
    mini = min(mini, sorted_r_minus_lmax[n-1-i])
    sorted_r_minus_lmax[n-1-i] = mini
rmin_minus_sorted_l = list(r[argrmin]-np.array(sorted_l))
mini = rmin_minus_sorted_l[0]
for i in range(1, n):
    mini = min(mini, rmin_minus_sorted_l[i])
    rmin_minus_sorted_l[i] = mini

ans2 = 0
for i in range(n-1):
    ai = max(0, sorted_r_minus_lmax[i+1])
    bi = max(0, rmin_minus_sorted_l[i])
    ans2 = max(ans2, ai+bi)

print(max(ans1, ans2))

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np

n = int(input())
l = []
r = []
ind = []
for i in range(n):
    li, ri = map(int, input().split())
    l.append(li)
    r.append(ri+1)
    ind.append(i)

arglmax = l.index(max(l))
argrmin = r.index(min(r))
num = 0
for i in range(n):
    num = max(r[i] - l[i], num)
ans1 = num + max(0, r[argrmin]-l[arglmax])

lst = [l, r, ind]
lst = list(np.array(lst).T)
lst = sorted(lst, key=lambda x: (x[0]), reverse=True)
lst = sorted(lst, key=lambda x: (x[1]))
lst = list(np.array(lst).T)
sorted_l = list(lst[0])
sorted_r = list(lst[1])
sorted_ind = list(lst[2])

ans2 = 0
for i in range(n-1):
    ai = max(0, min(np.array(sorted_r[i+1:])-l[arglmax]))
    bi = max(0, min(r[argrmin]-np.array(sorted_l[:i+1])))
    ans2 = max(ans2, ai+bi)

print(max(ans1, ans2))

Fixed submission:
import numpy as np

n = int(input())
l = []
r = []
for i in range(n):
    li, ri = map(int, input().split())
    l.append(li)
    r.append(ri+1)

arglmax = l.index(max(l))
argrmin = r.index(min(r))
num = 0
for i in range(n):
    num = max(r[i] - l[i], num)
ans1 = num + max(0, r[argrmin]-l[arglmax])

lst = [l, r]
lst = list(np.array(lst).T)
lst = sorted(lst, key=lambda x: (x[0]), reverse=True)
lst = sorted(lst, key=lambda x: (x[1]))
lst = list(np.array(lst).T)
sorted_l = list(lst[0])
sorted_r = list(lst[1])

sorted_r_minus_lmax = list(np.array(sorted_r)-l[arglmax])
mini = sorted_r_minus_lmax[n-1]
for i in range(1, n):
    mini = min(mini, sorted_r_minus_lmax[n-1-i])
    sorted_r_minus_lmax[n-1-i] = mini
rmin_minus_sorted_l = list(r[argrmin]-np.array(sorted_l))
mini = rmin_minus_sorted_l[0]
for i in range(1, n):
    mini = min(mini, rmin_minus_sorted_l[i])
    rmin_minus_sorted_l[i] = mini

ans2 = 0
for i in range(n-1):
    ai = max(0, sorted_r_minus_lmax[i+1])
    bi = max(0, rmin_minus_sorted_l[i])
    ans2 = max(ans2, ai+bi)

print(max(ans1, ans2))