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)

#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#define black_tree tree<ll,null_type,less_equal<ll>,rb_tree_tag,tree_order_statistics_node_update>
#define pair_black_tree tree<pair<ll,ll>,null_type,less<pair<ll,ll> >,rb_tree_tag,tree_order_statistics_node_update>
#define gp __gnu_pbds
#define INF 1000000000
#define MOD 1000000007
#define MAX 1000001
#define endl '\n'
#define ll long long
#define ld long double
#define lli long long int
#define ull unsigned long long
#define ulli unsigned long long int
#define pb push_back
#define pf push_front
#define ook order_of_key
#define fbo find_by_order
#define np next_permutation
#define mp make_pair
#define eb emplace_back
#define mae max_element
#define mie min_element
#define lb lower_bound 
#define ub upper_bound
#define bs binary_search
#define ff first
#define ss second
using namespace std;
using namespace gp;
vector<pair<ll,ll> >v;
ll n,x,y,ans=-1e50,dis=-1e50;
ll dist(pair<ll,ll> x,pair<ll,ll> y){
	return abs(x.ff-y.ff)+abs(x.ss-y.ss);
}
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cin>>n;
    for(int i=1;i<=n;i++){
    	cin>>x>>y;
    	v.pb({y,x});
	}
	sort(v.begin(),v.end());
	for(int i=0;i<v.size();i++){
		for(int j=i+1;j<v.size();j++){
			if(dist(v[i],v[j])>=dis){
				dis=dist(v[i],v[j]);
			}
			else{
				break;
			}
		}
		ans=max(dis,ans);
		dis=-1e50;
	}
	cout<<ans;
}