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 MOD 1000000007
typedef long long ll;
typedef pair<int, int> P;

int main(){
    int n;
    cin >> n;
    int a[n], b[n];
    for(int i=0; i<n; i++){
        cin >> a[i] >> b[i];
    }
    sort(a, a+n);
    sort(b, b+n);
    if(n%2 == 1){
        cout << b[n/2] - a[n/2]+1;
    }else{
        cout << b[n/2]+b[n/2-1] - (a[n/2]+a[n/2-1])+1;
    }
    return 0;
}