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>

using namespace std;
typedef long long ll;
const int N = 200010;
int d1[N], d2[N], n;

int main() {
    cin >> n;
    for (int i = 1; i <= n; i++) {
        int x, y;
        cin >> x >> y;
        d1[i] = x + y;
        d2[i] = x - y;
    }
    sort(d1 + 1, d1 + 1 + n);
    sort(d2 + 1, d2 + 1 + n);
    cout << max(d1[n] - d1[1], d2[n] - d2[1]) << '\n';
    return 0;
}
