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 <iostream>
#include <algorithm>
#include <vector>
using namespace std;
int main(void){
    using ll = long long;
    int n;
    cin >> n;
    ll a, b, c, d;
    a = c = 1e12;
    b = d = -1e12;

    for(int i=0;i<n;i++){
        ll x, y;
        cin >> x >> y;
        a = min(a, x+y);
        b = max(b, x+y);
        c = min(c, x-y);
        d = max(d, x-y);
    }
    cout << max(b-a, d-c) << endl;
}
