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(){
	ios::sync_with_stdio(0);
	cin.tie(0); cout.tie(0); 
	int N; cin >> N; 
	int A[200010], B[200010]; 
	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-1)/2] - A[(N-1)/2] + 1 << "\n"; 
	}else{
		int l = A[N/2] + A[N/2 - 1]; 
		int r = B[N/2] + B[N/2 - 1]; 
		cout << r - l + 1 << "\n"; 
	}
}