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 <vector>
#include <algorithm>
using namespace std;
vector<long long> u,v;
int main(){
    int i,n; cin >> n;
    for(i=0;i<n;i++){
        long long x,y; cin >> x >> y;
        u.push_back(x + y),v.push_back(x - y);
    }
    sort(u.begin(),u.end()); sort(v.begin(),v.end());
    long long ans = max(u[n - 1] - u[0],v[n - 1] - v[0]);
    cout << ans << endl;
}