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
#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0; i<(n); i++)
constexpr int MX = 200005;
int n, a[MX], b[MX], ans;
int main(){
	scanf("%d", &n);
	rep(i,n) scanf("%d%d", a+i, b+i);
	sort(a, a+n);
	sort(b, b+n);
	if(n % 2) ans = b[n/2] - a[n/2] + 1;
	else ans = b[n/2-1] - a[n/2-1] + b[n/2] - a[n/2] + 1;
	printf("%d\n", ans);
}