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.

Note

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.