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)

#pragma region template
#include <bits/stdc++.h>

#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define sz(a) (int)(a).size()
#define last(a) (a).at((int)(a).size()-1)
#define rep(i,n) for(int i=0,i##_len=(n);i<i##_len;i++)
#define brep(i,a,b) for(int i=(a),i##_len=(b);i<=i##_len;i++)
#define rrep(i,n) int i=(n);int now=-1;while(i--&&(now++||1))
#define xrep(i,n) for(int i=1,i##_len=(n);i<=i##_len;i++)
#define Yes(n) cout<<((n)?YES:NO)<<'\n'
#define co(n) cout<<(n)<<'\n'
#define Sort(v) sort(all(v))
#define rSort(v) sort(all(v),greater<typeof(v[0])>())
#define Rev(v) reverse(all(v))
#define Unique(v) (v).erase(unique(all(v)),(v).end())
#define eb emplace_back
#define fi first
#define se second

#ifdef ONLINE_JUDGE
#define here()
#define cprint(vec)
#define comment(msg)
#define observe(var)
#define local(x)
#define alter(x,y) y
#else
#define here() cerr<<__func__<<'/'<<__LINE__<<": passed\n"
#define cprint(vec) print_e(vec)
#define comment(msg) cerr<<"{ "<<msg<< " }\n"
#define observe(var) cerr<<"{ "<<#var<<" : "<<var<<" }\n"
#define local(x) x
#define alter(x,y) x
#endif

using namespace std;
using ll = long long;
using vll = vector<ll>;
using vbl = vector<bool>;
using vint = vector<int>;
using vvll = vector<vll>;
using vvbl = vector<vbl>;
using vdbl = vector<double>;
using vstr = vector<string>;
using vvint = vector<vint>;
using ull = unsigned long long;

constexpr int INF = 1e9;
constexpr ll LINF = 1e18;

// --- functions which take 1 argument --- //
inline void ignore_ret(int x){x++;}
template<class T> inline int sgn(const T& x){return (x>0)-(x<0);}
template<class T> inline int digit(T x){int r=1;while((x/=10)>=1)r++;return r;}
template<class T> inline double deg_to_rad(const T& a){return a/180.0*M_PI;}
template<class T> inline double rad_to_deg(const T& a){return a/M_PI*180.0;}
template<class T> inline ll factorial(const T& n){if(n==0)return 1;ll r=1;brep(i,2,n)r*=i;return r;}
template<class T> inline map<T,T> factorize(T n){map<T,T>r;for(T i=2;i*i<=n;i++){while(n%i==0){r[i]++;n/=i;}}if(n!=1)r[n]=1;return r;}
template<class T> inline vector<T> divisor(const T& n){vector<T>r;for(T i=1;i*i<=n;i++){if(!(n%i)){r.eb(i);if(i*i!=n)r.eb(n/i);}}Sort(r);return r;}

// --- functions which take 2 arguments --- //
template<class T> inline bool chmax(T& a,const T& b){if(a<b){a=b;return 1;}return 0;}
template<class T> inline bool chmin(T& a,const T& b){if(a>b){a=b;return 1;}return 0;}
template<class T> inline T nPr(const T& n,const T& k){if(n<k||n<0||k<0)return 0;T r=1;brep(i,n-k+1,n)r*=i;return r;}
template<class T> inline T nCr(const T& n,const T& k){if(n<k||n<0||k<0)return 0;T r=1;k=min(k,n-k);brep(i,n-k+1,n)r*=i;return r/factorial(k);}

// --- functions which take vector(s) as argument(s) --- //
template<class T> inline void print(const vector<T>& v){cout<<"[ ";for(auto& x:v)cout<<x<<' ';cout<<"]\n";}
template<class T> inline void print(const vector<vector<T>>& v){for(auto& x:v)print<T>(x);}
template<class T> inline void print_d(const vector<T>& v,string d){rep(i,sz(v)-1)cout<<v[i]<<d;cout<<last(v)<<'\n';}
template<class T> inline void print_d(const vector<vector<T>>& v,string d){for(auto& x:v)print_d(x,d);}
template<class T> inline void print_e(const vector<T>& v){cerr<<"[ ";for(auto& x:v)cerr<<x<<' ';cerr<<"]\n";}
template<class T> inline void print_e(const vector<vector<T>>& v){for(auto& x:v)print_e<T>(x);}
template<class S,class T> inline bool in(const S& k,const T& v){return find(all(v),k)!=v.end();}
template<class T> inline T min(const vector<T>& v){return *min_element(all(v));}
template<class T> inline T max(const vector<T>& v){return *max_element(all(v));}
template<class T> inline ll sum(const T& v){return reduce(all(v),0LL);}
template<class T> inline T gcd(const vector<T>& v){T r=v[0];brep(i,1,sz(v)-1)r=gcd(r,v[i]);return r;}
template<class T> inline T lcm(const vector<T>& v){T r=v[0];brep(i,1,sz(v)-1)r=lcm(r,v[i]);return r;}
template<class T> inline double abs(const vector<T>& v){return sqrt(reduce(all(v),0.0,[](T s,T v){return s+=v*v;}));}
template<class T> inline T vector_add(const T& u,const T& v){T r(u.size());rep(i,u.size())r[i]=u[i]+v[i];return r;}
template<class T> inline T vector_subtract(const T& u,const T& v){T r(u.size());rep(i,u.size())r[i]=u[i]-v[i];return r;}
template<class T> inline T vector_multiply(const T& u,const T& v){T r(u.size());rep(i,u.size())r[i]=u[i]*v[i];return r;}
template<class T> inline T dot_product(const vector<T>& u,const vector<T>& v){T r=0;rep(i,u.size())r+=u[i]*v[i];return r;}
template<class T> inline T cross_product(const T& u,const T& v){T r(3);rep(i,3)r[i]=u[(i+1)%3]*v[(i+2)%3]-u[(i+2)%3]*v[(i+1)%3];return r;}

// --- functions which take set/map as argument --- //
template<class T> inline void print(const set<T>& v){cout<<"[ ";for(T& x:v)cout<<x<<' ';cout<<"]\n";}
template<class T> inline bool in(const T& k,const vector<T>& v){return find(all(v),k)!=v.end();}
                  inline bool in(const int& k,const vector<ll>& v){return find(all(v),k)!=v.end();}
                  inline bool in(const ll& k,const vector<int>& v){return find(all(v),k)!=v.end();}
                  inline bool in(const char& k,const string& v){return find(all(v),k)!=v.end();}
                  inline bool in(const char*& k,const vector<string>& v){return find(all(v),k)!=v.end();}
template<class T> inline T min(const set<T>& v){return *min_element(all(v));}
template<class T> inline T max(const set<T>& v){return *max_element(all(v));}
template<class T> inline T gcd(const set<T>& v){T r=0;for(T x:v)r=(r==0)?x:gcd(r,x);return r;}
template<class T> inline T lcm(const set<T>& v){T r=0;for(T x:v)r=(r==0)?x:lcm(r,x);return r;}
template<class T> inline void print(const unordered_set<T>& v){cout<<"[ ";for(T& x:v)cout<<x<<' ';cout<<"]\n";}
template<class T> inline bool in(const T& k,const unordered_set<T>& v){return find(all(v),k)!=v.end();}
template<class T> inline T min(const unordered_set<T>& v){return *min_element(all(v));}
template<class T> inline T max(const unordered_set<T>& v){return *max_element(all(v));}
template<class T> inline T gcd(const unordered_set<T>& v){T r=0;for(T x:v)r=(r==0)?x:gcd(r,x);return r;}
template<class T> inline T lcm(const unordered_set<T>& v){T r=0;for(T x:v)r=(r==0)?x:lcm(r,x);return r;}
template<class S,class T> inline void print(const map<S,T>& m){cout<<"[ ";for(auto& x:m)cout<<"{ "<<x.fi<<", "<<x.se<<" } ";cout<<"]\n";}
template<class S,class T> inline void print(const unordered_map<S,T>& m){cout<<"[ ";for(auto& x:m)cout<<"{ "<<x.fi<<", "<<x.se<<" } ";cout<<"]\n";}

#pragma endregion template

bool cmp(const pair<ll,ll>& F, const pair<ll,ll>& S) {
  return F.second < S.second;
}

int main() {
  ll N;
  ignore_ret(scanf("%lld",&N));
  
  vector<ll> given(N);
  ll a, b;

  rep(i, N) {
    ignore_ret(scanf("%lld%lld",&a,&b));
    given[i] = b - a;
  }

  Sort(given);

  if (N % 2) {
    co(given[N/2] + 1);
  } else {
    co(given[N/2] + given[N/2-1] + 1);
  }
  
  return 0;
}