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.

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.

Examples

Input

2
1 2
2 3

Output

3

Input

3
100 100
10 10000
1 1000000000

Output

9991

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