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)

def main():

    N = int(input())
    AB = []
    for _ in range(N):
        A, B = map(int, input().split())
        AB.append([A, B])

    a = sorted(AB)
    # b = sorted(AB, key = lambda x: x[1])

    x, y = a[0]
    i = 1
    while i < (N+1)//2:
        z, w = a[i]
        if z > y:
            x, y = z, w
        elif x <= z <= y:
            x, y = z, min(y, w)
        i += 1

    # print(x, y)
    if N % 2 == 1:
        return y - x + 1
    return (y-x+1) + (y-x+1) // 2

if __name__ == '__main__':
    print(main())