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;
using ll = long long;

int main() {
	int n; scanf("%d", &n);
	vector<int> as(n), bs(n);
	for (int i = 0; i < n; ++i) scanf("%d %d", &as[i], &bs[i]);
	sort(begin(as), end(as));
	sort(begin(bs), end(bs));
	if (n % 2 == 1) {
		printf("%d\n", bs[n/2] - as[n/2] + 1);
	} else {
		printf("%lld\n", (ll)bs[n/2] + bs[n/2 - 1] - as[n/2] - as[n/2 - 1] + 1); 
	}
	return 0;
}
