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>
typedef long long ll;
using namespace std;
using Graph = vector< vector<int> >;

int main(){
	ll N;
	cin >> N;
	ll A[N],B[N];
	for (ll i = 0; i < N; i++)
	{
		cin >> A[i] >> B[i];
	}
	sort(A,A+N);
	sort(B,B+N);
	ll a,b;
	if(N%2 == 1){
		a = A[(N-1)/2];
		b = B[(N-1)/2];
		cout << b-a+1 << endl;
	}
	else{
		a=A[N/2-1]+A[N/2];
		b=B[N/2-1]+B[N/2];
		cout << b-a+1 << endl;
	}
}