Problem:
Score : 500 points

Problem Statement

There are N integers X_1, X_2, \cdots, X_N, and we know that A_i \leq X_i \leq B_i.
Find the number of different values that the median of X_1, X_2, \cdots, X_N can take.

Notes

The median of X_1, X_2, \cdots, X_N is defined as follows. Let x_1, x_2, \cdots, x_N be the result of sorting X_1, X_2, \cdots, X_N in ascending order.

If N is odd, the median is x_{(N+1)/2};

if N is even, the median is (x_{N/2} + x_{N/2+1}) / 2.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq A_i \leq B_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 B_1
A_2 B_2
:
A_N B_N

Output

Print the answer.

Sample Input 1

2
1 2
2 3

Sample Output 1

3

If X_1 = 1 and X_2 = 2, the median is \frac{3}{2};

if X_1 = 1 and X_2 = 3, the median is 2;

if X_1 = 2 and X_2 = 2, the median is 2;

if X_1 = 2 and X_2 = 3, the median is \frac{5}{2}.

Thus, the median can take three values: \frac{3}{2}, 2, and \frac{5}{2}.

Sample Input 2

3
100 100
10 10000
1 1000000000

Sample Output 2

9991

Solution in Python (3.8.2) (judge verdict: Wrong Answer)

n=int(input())
ab = []
for _ in range(n):
    a,b=map(int,input().split())
    ab.append((a,b))


pool = []
for a,b in ab:
    af = sum([1 for a1,b1 in list(ab) if a1 <= a <= b1])
    bf = sum([1 for a1,b1 in list(ab) if a1 <= b <= b1])
    pool.append((a,af))
    pool.append((b, bf))

# print(pool)

max_pool = max([p[1] for p in pool])
pool = [p[0] for p in pool if p[1] >= max_pool-1]
# print(pool)

if max_pool%2 == 1:
    print(max(pool) - min(pool) + 1)
else:
    print(max(pool) - min(pool) + 1)