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-----
2
1 2
2 3

-----Sample Output-----
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 $\frac{5}{2}$.

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