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 Julia (1.4.0) (judge verdict: Accepted)

const double = Float64
const int = Int64

parseint(x) = parse(int, x)
readint() = map(parseint, split(readline()))

function main()
  n = readint()[1]
  A = Vector{int}(undef,n)
  B = Vector{int}(undef,n)

  for i in 1:n
    A[i], B[i] = readint()
  end
  
  sort!(A)
  sort!(B)

  if n%2 == 1
    println(B[n÷2 + 1] - A[n÷2 + 1] + 1)
  else
    println(B[n÷2] + B[n÷2 + 1] - A[n÷2] - A[n÷2 + 1]+1)
  end
  #println()
end

main()