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;

void solve() {
    int n;
    cin >> n;
    
    int a[n], b[n];
    for(int i=0; i<n; i++) {
        int u, v;
        cin >> u >> v;
        a[i] = u+v;
        b[i] = u-v;
    }
    
    sort(a, a+n);
    sort(b, b+n);
    
    cout << max(abs(a[n-1]-a[0]), abs(b[n-1]-b[0])) << endl;
}

int main() {
	// your code goes here
	
	solve();
	
	return 0;
}
