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;
const int maxn=2e5+5;
int x[maxn],y[maxn];
int main(){ 
     int n;
     scanf("%d",&n);
     for(int i=1;i<=n;++i){ 
        int a,b;
        scanf("%d%d",&a,&b);
        x[i]=a+b;y[i]=a-b;
     }
     sort(x+1,x+1+n);
     sort(y+1,y+1+n);
     cout<<max(y[n]-y[1],x[n]-x[1])<<endl;
}
