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 statistics
f = statistics.median
N = int(input())

a = [0]*N
b = [0]*N

for i in range(N):
    m, n = map(int, input().split())
    a[i] = m
    b[i] = n

if N % 2 == 1:
    print(int(f(b)-f(a)+1))
else:
    print(int(f(b)*2-f(a)*2+1))