p02874 AtCoder Grand Contest 040 - Two Contests
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
```python
# python template for atcoder1
import sys
sys.setrecursionlimit(10**9)
input = sys.stdin.readline


class SegmentTree():
    '''
    非再帰
    segment tree
    '''

    def __init__(self, n, func, init=float('inf')):
        '''
        n->配列の長さ
        func:func(a,b)->val,　func=minだとRMQになる
        木の高さhとすると,
        n:h-1までのノード数。h段目のノードにアクセスするために使う。
        data:ノード。
        parent:k->child k*2+1とk*2+2
        '''
        self.n = 2**(n-1).bit_length()
        self.init = init
        self.data = [init]*(2*self.n)
        self.func = func

    def set(self, k, v):
        '''
        あたいの初期化
        '''
        self.data[k+self.n-1] = v

    def build(self):
        '''
        setの後に一斉更新
        '''
        for k in reversed(range(self.n-1)):
            self.data[k] = self.func(self.data[k*2+1], self.data[k*2+2])

    def update(self, k, a):
        '''
        list[k]=aに更新する。
        更新ぶんをrootまで更新
        '''
        k += self.n-1
        self.data[k] = a

        while k > 0:
            k = (k-1)//2
            self.data[k] = self.func(self.data[k*2+1], self.data[k*2+2])

    def query(self, l, r):
        '''
        [l,r)のfuncを求める
        '''
        L = l+self.n
        R = r+self.n
        ret = self.init
        while L < R:
            if R & 1:
                R -= 1
                ret = self.func(ret, self.data[R-1])
            if L & 1:
                ret = self.func(ret, self.data[L-1])
                L += 1
            L >>= 1
            R >>= 1
        return ret


N = int(input())
L = [list(map(int, input().split())) for _ in range(N)]
L = sorted(L, key=lambda x: x[0])

Seg_L = SegmentTree(N, lambda a, b: max(a, b), init=0)
Seg_R = SegmentTree(N, lambda a, b: min(a, b), init=float('inf'))

for i, q in enumerate(L):
    l, r = q[0], q[1]
    Seg_L.set(i, l)
    Seg_R.set(i, r)
Seg_L.build()
Seg_R.build()
cand = []
for pivot in range(1, N):
    low_1, high_1 = Seg_L.query(0, pivot), Seg_R.query(0, pivot)
    low_2, high_2 = Seg_L.query(pivot, N), Seg_R.query(pivot, N)
    p1 = max(high_1-low_1+1, 0)
    p2 = max(high_2-low_2+1, 0)
    ans = p1+p2
    cand.append(ans)
ans1 = max(cand)

cand2 = []
for rem in range(N):
    rem_low = Seg_L.query(rem, rem+1)
    rem_high = Seg_R.query(rem, rem+1)
    use_low = max(Seg_L.query(0, rem), Seg_L.query(rem+1, N))
    use_high = min(Seg_R.query(0, rem), Seg_R.query(rem+1, N))
    p1 = max(rem_high-rem_low+1, 0)
    p2 = max(use_high-use_low+1, 0)
    ans = p1+p2
    cand2.append(ans)
ans2 = max(cand2)
print(max(ans1, ans2))

```