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;
int main()
{

ll n,ans1,ans2,k,kk,p,pp;
cin>>n;
ll a[n],b[n],c[n],d[n];
for(int i=0;i<n;i++)
{
    cin>>a[i]>>b[i];
    c[i]=a[i]+b[i];
    d[i]=a[i]-b[i];
}
sort(c,c+n);
k=*max_element(c,c+n);
kk=*min_element(c,c+n);
p=*max_element(d,d+n);
pp=*min_element(d,d+n);
ans1=k-kk;
ans2=p-pp;
cout<<max(ans1,ans2)<<endl;
}
