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.

Examples

Input

3
1 1
2 4
3 2


Output

4


Input

2
1 1
1 1


Output

0
#include<bits/stdc++.h>
#define ll long long int
#define mod 1000000007
using namespace std;

int main(){
	
	int n;
	cin>>n;
	map<ll,ll>mp1,mp2;
	while(n--){
		ll x,y;
		cin>>x>>y;
		mp1[x+y]++;
		mp2[x-y]++;
	}
	ll res=abs(mp1.rbegin()->first-mp1.begin()->first);
	res=max(res,mp2.rbegin()->first-mp2.begin()->first);
	cout<<res<<endl;
	return 0;
}
