Problem:
Score : 500 points

Problem Statement

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.

Notes

The median of X_1, X_2, \cdots, X_N is defined as follows. Let x_1, x_2, \cdots, x_N be the result of sorting X_1, X_2, \cdots, X_N in ascending order.

If N is odd, the median is x_{(N+1)/2};

if N is even, the median is (x_{N/2} + x_{N/2+1}) / 2.

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.

Sample Input 1

2
1 2
2 3

Sample Output 1

3

If X_1 = 1 and X_2 = 2, the median is \frac{3}{2};

if X_1 = 1 and X_2 = 3, the median is 2;

if X_1 = 2 and X_2 = 2, the median is 2;

if X_1 = 2 and X_2 = 3, the median is \frac{5}{2}.

Thus, the median can take three values: \frac{3}{2}, 2, and \frac{5}{2}.

Sample Input 2

3
100 100
10 10000
1 1000000000

Sample Output 2

9991

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

// Hail god Yato
 
#include <bits/stdc++.h> 
using namespace std;
 
#define hs ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
typedef long long ll;
const ll MOD = 1000000007;
const ll INF = 1e18;
const ll MAX = 100001;
//
//
void solve(){
    int n;
    cin>>n;
    vector<ll> fst(n), snd(n);
    for(int i = 0; i < n; i++)
        cin>>fst[i]>>snd[i];
    double fstmedian, sndmedian;
    sort(fst.begin(), fst.end());
    sort(snd.begin(), snd.end());
    if(n&1){
        fstmedian = fst[n/2];
        sndmedian = snd[n/2];
        cout<<sndmedian - fstmedian+1;
    }
    else{
        fstmedian = (fst[n/2-1] + fst[n/2])/2.00;
        sndmedian = (snd[n/2 -1] + snd[n/2])/2.00;
        // fstmedian = 1.5, sndmedian = 3;
        cout<<2*(int(sndmedian - fstmedian)) + 1;
    }
}
int main(){ 
        hs;
        ll t;
        t=1;
        // cin>>t;
        for (int i=1; i<=t; i++){
                //cout<<"Case #"<<i<<": ";
                solve();
         }
        return 0; 
}