Problem:
Score : 500 points

Problem Statement

There are N points on the 2D plane, i-th of which is located on (x_i, y_i).
There can be multiple points that share the same coordinate.
What is the maximum possible Manhattan distance between two distinct points?

Here, the Manhattan distance between two points (x_i, y_i) and (x_j, y_j) is defined by |x_i-x_j| + |y_i-y_j|.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq x_i,y_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print the answer.

Sample Input 1

3
1 1
2 4
3 2

Sample Output 1

4

The Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.

Sample Input 2

2
1 1
1 1

Sample Output 2

0

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

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define lvector vector<ll>
#define cvector vector<char>
#define svector vector<string>
#define lque queue<ll>
#define lpque priority_queue<ll>
#define dlpque priority_queue<ll,lvector,greater<ll>>
#define P pair<ll,ll>
#define ALL(a) a.begin(),a.end()
#define RALL(a) a.rbegin(),a.rend()
#define rep(i,n) for(ll i=0; i<n; ++i)
#define print(a) cout << (a) << endl

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  ll n,x,y;cin>>n;
  vector<P> v(n),w(n);
  rep(i,n) {cin>>x>>y;v[i]=P(x,y);w[i]=P(y,x);}
  sort(ALL(v));
  ll ans=0,tmp;
  for(ll i=1;i<n;++i) {
    tmp=abs(v[i].first-v[0].first)+abs(v[i].second-v[0].second);
    ans=max(ans,tmp);
  }
  for(ll i=0;i<n-1;++i) {
    tmp=abs(v[n-1].first-v[i].first)+abs(v[n-1].second-v[i].second);
    ans=max(ans,tmp);
  }
  for(ll i=1;i<n;++i) {
    tmp=abs(w[i].first-w[0].first)+abs(w[i].second-w[0].second);
    ans=max(ans,tmp);
  }
  for(ll i=0;i<n-1;++i) {
    tmp=abs(w[n-1].first-w[i].first)+abs(w[n-1].second-w[i].second);
    ans=max(ans,tmp);
  }
  print(ans);
  return 0;
}