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 n, x[200005], y[200005], a[200005], b[200005];

int main(){
    scanf("%d", &n);
    for (int i = 0; i < n; ++i){
        scanf("%d%d", &x[i], &y[i]);
    }
    for (int i = 0; i < n; ++i){
        a[i] = x[i] + y[i];
        b[i] = x[i] - y[i];
    }
    sort(a, a + n);
    sort(b, b + n);
    int ans = max(a[n - 1] - a[0], b[n - 1] - b[0]);
    printf("%d", ans);
}
