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 main() {
    int N;
    cin >> N;
    long a, b;
    vector<long> p, q;
    for (int i = 0; i < N; ++i) {
        cin >> a >> b;
        p.push_back(a + b);
        q.push_back(a - b);
    }
    sort(p.begin(), p.end(), less<int>());
    sort(q.begin(), q.end(), less<int>());
    cout << max(*p.rbegin() - *p.begin(), *q.rbegin() - *q.begin()) << endl;
    return 0;
}
