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
import sys
read = sys.stdin.buffer.read
N, *AB = map(int, read().split())
A,B=AB[::2],AB[1::2]
A.sort()
B.sort(reverse=True)
pos=(N+1)//2-1
if N%2==1:
    ans = B[pos]-A[pos]+1
else:
    ans = (B[pos]+B[pos+1])-(A[pos]+A[pos+1])+1
print(ans)