Buggy python submission (verdict: Runtime Error):
N = int(input())
LR = []
p = 0
max_L = 0
q = 0
min_R = 10**9 + 1

for i in range(N):
    L, R = map(int, input().split())
    R += 1
    LR.append((L, R))
    if L > max_L:
        p = i
        max_L = L
    if R < min_R:
        q = i
        min_R = R

if p == q:
    print(max(r - l for l, r in LR) + max(min_R - max_L, 0))
    exit()

L1, R1 = LR[p]
L2, R2 = LR[q]
LR = [(L, R) for i, (L, R) in enumerate(LR) if i != p and i != q]
LR.sort(key=lambda x: (x[1], x[0]), reverse=True)

ans1 = max(R - L for L, R in LR) + max(min_R - max_L, 0)

n = len(LR) + 1
min_sr = [R1] * n
max_tl = [L2] * n

for i in range(1, n):
    min_sr[i] = min(min_sr[i-1], LR[i-1][1])
    max_tl[n-i-1] = max(max_tl[n-i], LR[n-i-1][0])

ans2 = max(max(r - L1, 0) + max(R2 - l, 0) for r, l in zip(min_sr, max_tl))

print(max(ans1, ans2))


Fixed submission:
N = int(input())
LR = []
p = 0
max_L = 0
q = 0
min_R = 10**9 + 1

for i in range(N):
    L, R = map(int, input().split())
    R += 1
    LR.append((L, R))
    if L > max_L:
        p = i
        max_L = L
    if R < min_R:
        q = i
        min_R = R

ans1 = max(R - L for L, R in LR) + max(min_R - max_L, 0)

if N == 2:
    print(sum(R - L for L, R in LR))
    exit()

if p == q:
    print(ans1)
    exit()

L1, R1 = LR[p]
L2, R2 = LR[q]
LR = [(L, R) for i, (L, R) in enumerate(LR) if i != p and i != q]
LR.sort(key=lambda x: (x[1], x[0]), reverse=True)

n = len(LR) + 1
min_sr = [R1] * n
max_tl = [L2] * n

for i in range(1, n):
    min_sr[i] = min(min_sr[i-1], LR[i-1][1])
    max_tl[n-i-1] = max(max_tl[n-i], LR[n-i-1][0])

ans2 = max(max(r - L1, 0) + max(R2 - l, 0) for r, l in zip(min_sr, max_tl))

print(max(ans1, ans2))

Buggy python submission (verdict: Runtime Error):
def calc(s, t):
    t_l = [x[0] for x in t]
    s_r = [x[1] for x in s]
    return max(min(s_r) - max_L, 0) + max(min_R - max(t_l), 0)


N = int(input())
sections = []

L, R = map(int, input().split())
sections.append((L, R + 1))
p = 0
max_L = L
q = 0
min_R = R

for i in range(1, N):
    L, R = map(int, input().split())
    R += 1
    sections.append((L, R))
    if L > max_L:
        p = i
        max_L = L
    if R < min_R:
        q = i
        min_R = R

s = [sections[p]]
t = [sections[q]]
sections.pop(p)
sections.sort(key=lambda x: (x[1], x[0]))
sections.pop(0)  # q
s = sections + s

ranges = [x[1] - x[0] for x in sections]
ans1 = max(ranges) + max(min_R - max_L, 0)

ans2 = calc(s, t)

for i in range(len(sections)):
    t += [s.pop(0)]
    ans2 = max(ans2, calc(s, t))

print(max(ans1, ans2))


Fixed submission:
N = int(input())
LR = []
p = 0
max_L = 0
q = 0
min_R = 10**9 + 1

for i in range(N):
    L, R = map(int, input().split())
    R += 1
    LR.append((L, R))
    if L > max_L:
        p = i
        max_L = L
    if R < min_R:
        q = i
        min_R = R

ans1 = max(R - L for L, R in LR) + max(min_R - max_L, 0)

if N == 2:
    print(sum(R - L for L, R in LR))
    exit()

if p == q:
    print(ans1)
    exit()

L1, R1 = LR[p]
L2, R2 = LR[q]
LR = [(L, R) for i, (L, R) in enumerate(LR) if i != p and i != q]
LR.sort(key=lambda x: (x[1], x[0]), reverse=True)

n = len(LR) + 1
min_sr = [R1] * n
max_tl = [L2] * n

for i in range(1, n):
    min_sr[i] = min(min_sr[i-1], LR[i-1][1])
    max_tl[n-i-1] = max(max_tl[n-i], LR[n-i-1][0])

ans2 = max(max(r - L1, 0) + max(R2 - l, 0) for r, l in zip(min_sr, max_tl))

print(max(ans1, ans2))