Problem:
Score : 500 points

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.

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 1

2
1 2
2 3

Sample Output 1

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 Input 2

3
100 100
10 10000
1 1000000000

Sample Output 2

9991

Solution in Python (3.8.2) (judge verdict: Accepted)

## coding: UTF-8
import statistics
#import math

N = int(input())
#lq = [list(map(int, input().split())) for _ in range(N)]
#print(lq)

A = []
B = []
for i in range(N):
    a, b = map(int,input().split())
    A.append(a)
    B.append(b)
#print(A)
#print(B)

#l = [10, 1, 3, 7, 1]

#median = statistics.median(l)
#print(median)

if(N%2 == 1):
    lowest = statistics.median(A)
    highest = statistics.median(B)
    ans = highest - lowest + 1
else:
    lowest = statistics.median(A)
    highest = statistics.median(B)
    ans = (2 * highest) - (2 * lowest) + 1

print(int(ans))