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() {
	long long N;
	cin >> N;
	vector<long long> 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());
	long long P = A[(N - 1) / 2] + A[N / 2], Q = B[(N - 1) / 2] + B[N / 2];
	if (N % 2 == 1) cout << Q / 2 - P / 2 + 1 << endl;
	else cout << Q - P + 1 << endl;
}