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 <iostream>
#include <vector>
#include <algorithm>

using namespace std;

int main() {
    int n;
    cin >> n;

    vector<int> a(n), b(n);
    for (int i = 0; i < n; i++)cin >> a[i] >> b[i];
    sort(a.begin(), a.end()), sort(b.begin(), b.end());

    if (n % 2 == 1)cout << b[n / 2] - a[n / 2] + 1 << endl;
    else cout << (b[n / 2] + b[n / 2 - 1]) - (a[n / 2] + a[n / 2 - 1]) + 1 << endl;
    return 0;
}