Buggy python submission (verdict: Runtime Error):
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
    res = list(sys.stdin.readline())
    if res[-1] == "\n":
        return res[:-1]
    return res
def IR(n):
    return [I() for i in range(n)]
def LIR(n):
    return [LI() for i in range(n)]
def SR(n):
    return [S() for i in range(n)]
def LSR(n):
    return [LS() for i in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007

class SlidingWindowAggretgation:
    def __init__(self, default, f = min):
        self.default = default
        self.f = f
        self.front_stack = deque()
        self.back_stack = deque()

    def get(self):
        res = self.default
        if self.front_stack:
            res = self.f(res, self.front_stack[-1][1])
        if self.back_stack:
            res = self.f(res, self.back_stack[-1][1])
        return res

    def append(self, x):
        fx = x
        if self.back_stack:
            fx = self.f(self.back_stack[-1][1], x)
        self.back_stack.append((x, fx))

    def popleft(self):
        if not self.front_stack:
            x, fx = self.back_stack.pop()
            self.front_stack.append((x, x))
            while self.back_stack:
                x, fx = self.back_stack.pop()
                fx = self.f(x, self.front_stack[-1][1])
                self.front_stack.append((x, fx))
        self.front_stack.pop()

def solve():
    n = I()
    p = LIR(n)
    p.sort()
    maxl = max([l for (l,r) in p])
    minr = min([r for (l,r) in p])
    ans = max(0, minr-maxl+1)+max([r-l+1 for (l,r) in p if l != maxl and r != minr])
    swagll = SlidingWindowAggretgation(0,max)
    swaglr = SlidingWindowAggretgation(float("inf"),min)
    swagrl = SlidingWindowAggretgation(0,max)
    swagrr = SlidingWindowAggretgation(float("inf"),min)
    for l,r in p:
        swagrl.append(l)
        swagrr.append(r)
    for l,r in p[:-1]:
        swagll.append(l)
        swaglr.append(r)
        swagrl.popleft()
        swagrr.popleft()
        ll = swagll.get()
        lr = swaglr.get()
        rl = swagrl.get()
        rr = swagrr.get()
        k = max(lr-ll+1,0)+max(rr-rl+1,0)
        if ans < k:
            ans = k
    print(ans)
    return

#Solve
if __name__ == "__main__":
    solve()


Fixed submission:
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
    res = list(sys.stdin.readline())
    if res[-1] == "\n":
        return res[:-1]
    return res
def IR(n):
    return [I() for i in range(n)]
def LIR(n):
    return [LI() for i in range(n)]
def SR(n):
    return [S() for i in range(n)]
def LSR(n):
    return [LS() for i in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007

class SlidingWindowAggretgation:
    def __init__(self, default, f = min):
        self.default = default
        self.f = f
        self.front_stack = deque()
        self.back_stack = deque()

    def get(self):
        res = self.default
        if self.front_stack:
            res = self.f(res, self.front_stack[-1][1])
        if self.back_stack:
            res = self.f(res, self.back_stack[-1][1])
        return res

    def append(self, x):
        fx = x
        if self.back_stack:
            fx = self.f(self.back_stack[-1][1], x)
        self.back_stack.append((x, fx))

    def popleft(self):
        if not self.front_stack:
            x, fx = self.back_stack.pop()
            self.front_stack.append((x, x))
            while self.back_stack:
                x, fx = self.back_stack.pop()
                fx = self.f(x, self.front_stack[-1][1])
                self.front_stack.append((x, fx))
        self.front_stack.pop()

def solve():
    n = I()
    p = LIR(n)
    p.sort()
    maxl = max([l for (l,r) in p])
    minr = min([r for (l,r) in p])
    ans = max(0, minr-maxl+1)+max([r-l+1 for (l,r) in p])
    swagll = SlidingWindowAggretgation(0,max)
    swaglr = SlidingWindowAggretgation(float("inf"),min)
    swagrl = SlidingWindowAggretgation(0,max)
    swagrr = SlidingWindowAggretgation(float("inf"),min)
    for l,r in p:
        swagrl.append(l)
        swagrr.append(r)
    for l,r in p[:-1]:
        swagll.append(l)
        swaglr.append(r)
        swagrl.popleft()
        swagrr.popleft()
        ll = swagll.get()
        lr = swaglr.get()
        rl = swagrl.get()
        rr = swagrr.get()
        k = max(lr-ll+1,0)+max(rr-rl+1,0)
        if ans < k:
            ans = k
    print(ans)
    return

#Solve
if __name__ == "__main__":
    solve()