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>
#define ll long long
using namespace std;
ll a[10101010],b[10101010];
int main() {
    int n;
    cin >>n;
    for (int i = 0; i < n;i ++)
		cin >>a[i] >>b[i];
    sort(a,a + n);
    sort(b,b + n);
    if (n % 2 == 0) {
        cout <<(b[n / 2 - 1] + b[n / 2] - a[n / 2 - 1] - a[n / 2] + 1);
    }
	else {
        cout <<(b[n / 2] - a[n / 2] + 1);
    }
}