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
#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using v=vector<int>;

int main() {
    int N;cin>>N;
    v x(N);
    v y(N);
    for (int i = 0; i < N; i++){
        int X,Y;cin>>X>>Y;
        x[i]=X+Y;
        y[i]=X-Y;
    }
    sort(x.begin(),x.end());
    sort(y.begin(),y.end());
    cout<<max(x[N-1]-x[0],y[N-1]-y[0])<<endl;
}