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>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;

int main(){
	ll n;
	cin>>n;
	ll ma1=-1e15,ma2=-1e15,mi1=1e15,mi2=1e15;
	for(int i=0;i<n;i++){
		ll a,b;
		cin>>a>>b;
		ma1=max(ma1,a+b);
		ma2=max(ma2,a-b);
		mi1=min(mi1,a+b);
		mi2=min(mi2,a-b);
	}
	cout<<max(ma1-mi1,ma2-mi2);
	return 0;
}
