human
10^9 contestants, numbered 1 to 10^9, will compete in a competition. There will be two contests in this competition.

The organizer prepared N problems, numbered 1 to N, to use in these contests. When Problem i is presented in a contest, it will be solved by all contestants from Contestant L_i to Contestant R_i (inclusive), and will not be solved by any other contestants.

The organizer will use these N problems in the two contests. Each problem must be used in exactly one of the contests, and each contest must have at least one problem.

The joyfulness of each contest is the number of contestants who will solve all the problems in the contest. Find the maximum possible total joyfulness of the two contests.

Constraints

* 2 \leq N \leq 10^5
* 1 \leq L_i \leq R_i \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
L_1 R_1
L_2 R_2
\vdots
L_N R_N

Output

Print the maximum possible total joyfulness of the two contests.

Examples

Input

4
4 7
1 4
5 8
2 5

Output

6

Input

4
1 20
2 19
3 18
4 17

Output

34

Input

10
457835016 996058008
456475528 529149798
455108441 512701454
455817105 523506955
457368248 814532746
455073228 459494089
456651538 774276744
457667152 974637457
457293701 800549465
456580262 636471526

Output

540049931
Solve the task in PYTHON3.

Can you provide a Python program to find the maximum possible total joyfulness of the two contests?
assistant
#Here is Python program to find the maximum possible total joyfulness of the two contests.

# -*- coding: utf-8 -*-
import bisect
import heapq
import math
import random
import sys
from collections import Counter, defaultdict, deque
from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
from functools import lru_cache, reduce
from itertools import combinations, combinations_with_replacement, product, permutations
from operator import add, mul, sub

sys.setrecursionlimit(100000)
input = sys.stdin.readline
INF = 2**62-1

def read_int():
    return int(input())

def read_int_n():
    return list(map(int, input().split()))

def read_float():
    return float(input())

def read_float_n():
    return list(map(float, input().split()))

def read_str():
    return input().strip()

def read_str_n():
    return list(map(str, input().split()))

def error_print(*args):
    print(*args, file=sys.stderr)

def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.time()
        ret = f(*args, **kwargs)
        e = time.time()

        error_print(e - s, 'sec')
        return ret

    return wrap

@mt
def slv(N, LR):
    LR.sort(key=lambda x: x[1])
    LR.sort(key=lambda x: x[0])

    lc = []
    l = 0
    r = INF
    for i in range(N):
        l_, r_ = LR[i]
        l = max(l, l_)
        r = min(r, r_)
        lc.append((l, r))
    
    rc = []
    l = 0
    r = INF
    for i in range(N-1, -1, -1):
        l_, r_ = LR[i]
        l = max(l, l_)
        r = min(r, r_)
        rc.append((l, r))
    
    def c(l, r):
        return max(0, r-l+1)

    ans = 0
    for i in range(N-1):
        ans = max(ans, c(*lc[i]) + c(*rc[N-1-1-i]))
    for i in range(N):
        tmp = c(*LR[i])
        l, r = (0, INF)
        if i != 0:
            l = max(l, lc[i-1][0])
            r = min(r, lc[i-1][1])
        if i != N-1:
            l = max(l, rc[N-1-i][0])
            r = min(r, rc[N-1-i][1])
            
        tmp += c(l, r)
        ans = max(ans, tmp)

    return ans

def main():
    N = read_int()
    LR = [read_int_n() for _ in range(N)]
    print(slv(N, LR))

if __name__ == '__main__':
    main()