
Score : 500 points
Problem StatementThere 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.
NotesThe 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.
InputInput is given from Standard Input in the following format:
N
A_1 B_1
A_2 B_2
:
A_N B_N
OutputPrint the answer.
Sample Input 12
1 2
2 3
Sample Output 13
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 23
100 100
10 10000
1 1000000000
Sample Output 29991
