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 x[200005], y[200005];
int X[200005], Y[200005];
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    int n;
    cin >> n;
    for(int i=1;i<=n;i++){
        cin >> x[i] >> y[i];
        X[i] = x[i]+y[i], Y[i] = x[i]-y[i];
    }
    sort(X+1, X+1+n);
    sort(Y+1, Y+1+n);
    int ans = max(X[n]-X[1], Y[n]-Y[1]);
    printf("%d\n", ans);
}