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;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

int main(void){
    int n;
    cin >> n;
    int x[n],y[n];
    rep(i,n) cin >> x[i] >> y[i];
    int x1[n],y1[n];
    rep(i,n){
        x1[i] = x[i]+y[i];
        y1[i] = x[i]-y[i]; 
    } 
    sort(x1,x1+n);
    sort(y1,y1+n);
    cout << max(x1[n-1]-x1[0],y1[n-1]-y1[0]) << endl;
}