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;
int main() {
	int n;
	scanf("%d", &n);
	vector<int> a(n), b(n);
	for(int i = 0; i < n; ++i) {
		scanf("%d%d", &a[i], &b[i]);
	}
	sort(a.begin(), a.end());
	sort(b.begin(), b.end());
	int low = a[(n-1)/2] + a[n/2];
	int high = b[(n-1)/2] + b[n/2];
	int answer = high - low + 1;
	if(n % 2 == 1) {
		answer = (answer + 1) / 2;
	}
	printf("%d\n", answer);
}
