6872: ABC169 —— E - Count Median
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Description
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 $(x_{N/2} + x_{N/2+1}) / 2$.
Input
Input is given from Standard Input in the following format:
$N$
$A_1\ B_1$
$A_2\ B_2$
$\vdots$
$A_N\ B_N$
$N$
$A_1\ B_1$
$A_2\ B_2$
$\vdots$
$A_N\ B_N$
Output
Print the answer.
Constraints
$2≤N≤2×10^5$
$1 \leq A_i \leq B_i \leq 10^9$
All values in input are integers.
$1 \leq A_i \leq B_i \leq 10^9$
All values in input are integers.
Sample 1 Input
2
1 2
2 3
Sample 1 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 $\frac{5}{2}$.
Sample 2 Input
3
100 100
10 10000
1 1000000000
Sample 2 Output
9991