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()
  {int N; cin >> N;
  vector<int> A(N), B(N); for (int i = 0; i < N; ++i) cin >> A[i] >> B[i]; sort(begin(A), end(A)); sort(begin(B), end(B));
  auto m = (N - 1) / 2; cout << (N % 2 ? B[m] - A[m] + 1 : B[m] + B[m + 1] - (A[m] + A[m + 1]) + 1) << endl;}