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)

int main() {
	int N;
	cin >> N;
	vector<int> A(N),B(N);

	rep(i,N)
		cin >> A.at(i) >> B.at(i);
	sort(A.begin(), A.end());
	sort(B.begin(), B.end());
	
	if(N%2)
		cout << B.at(N/2)-A.at(N/2)+1;
	else
		cout << B.at(N/2)+B.at(N/2-1)-A.at(N/2)-A.at(N/2-1)+1;
	cout << endl;
}