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;

int main() {
    int n;
    cin>>n;
    //take positive and negative array to store x+y (+ +) and x-y (+ -)
    long long int pa[n], na[n];
    for(int i = 0; i < n; i++) {
        long long int a, b;
        cin>>a>>b;
        pa[i] = a+b;
        na[i] = a-b;
    }
    sort(pa, pa+n);
    sort(na, na+n);
    cout<<max(pa[n-1] - pa[0], na[n-1]-na[0])<<endl;
    return 0;
}