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: Accepted)

#include <bits/stdc++.h>
using namespace std;

#define ll long long

#define all(x) x.begin(), x.end()
#define allr(x) x.rbegin(), x.rend()
#define fill(a,b) memset(a,b,sizeof(a))

#define f first
#define s second
#define pb push_back

#define inf 1e17
#define ninf -1*1e17
#define mod 1000000007
#define N 500005
#define Ns 5005

// string s;
ll n,m,o,z,d,k,l,r;

ll dp[N];
int main() {
    
    ios_base::sync_with_stdio(false);
    cin.tie(NULL); cout.tie(NULL);
    
	int t=1;
	//cin>>t;
	while(t--){
	    
	    ll ans=0;
	    cin>>n;
	    int x[n],y[n];
	    set<pair<ll,ll>>s;
	    for(int i=0;i<n;i++){
	        int x1,y1;
	        cin>>x1>>y1;
	        s.insert({x1,y1});
	    }
	    ll mi=inf,mi2=inf;
	    for(auto it=s.begin();it!=s.end();it++){
	        
	        if(it==s.begin()){
	            mi=(*it).f+(*it).s;
	            mi2=(*it).f-(*it).s;
	            continue;
	        }
	       // cout<<*it<<" %\n";
	        ll cur=(*it).f+(*it).s;
	        ll cur2=(*it).f-(*it).s;
	        ans=max(ans,cur-mi);
	        ans=max(ans,cur2-mi2);
	        
	        mi=min(mi,cur);
	        mi2=min(mi2,cur2);
	        
	    }
	    cout<<ans;
	}
	    
	return 0;
}