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;

int main() {
    int N;
    cin >> N;
    vector<int> arr1(N), arr2(N);
    int x, y;
    for (int i = 0; i < N; i++) {
        cin >> x >> y;
        arr1[i] = x + y;
        arr2[i] = x - y;
    }
    sort(arr1.begin(), arr1.end());
    sort(arr2.begin(), arr2.end());
    cout << max(arr1[N - 1] - arr1[0], arr2[N - 1] - arr2[0]) << endl;
}