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;

const int N=2e5+20;

int n,x,y;
vector <int> vx,vy;

int main()
{
	scanf("%d",&n);
	for(int i=0;i<n;i++)
	{
		scanf("%d%d",&x,&y);
		vx.push_back(x);
		vy.push_back(y);
	}

	sort(vx.begin(),vx.end());
	sort(vy.begin(),vy.end());

	if(n&1) printf("%d",vy[n/2]-vx[n/2]+1);
	else printf("%d",vy[n/2-1]+vy[n/2]-(vx[n/2-1]+vx[n/2])+1);
}