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;
long long a,b,c,d,i,e,f,g,n,m,k,l,A[500005],B[500005];
int main() {
    cin>>n;
    for(long long i=1;i<=n;i++) {
        cin>>a>>b;
        A[i]=a+b;
        B[i]=a-b;
    }
    sort(A+1,A+1+n);
    sort(B+1,B+1+n);
    cout<<max(A[n]-A[1],B[n]-B[1]);
}