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,x,y,w,w1,ma=-2e9,ma1=-2e9,mi=2e9,mi1=2e9;scanf("%d",&n);
	for(int i=0;i<n;i++){
		scanf("%d%d",&x,&y);
		w=x+y,w1=x-y;
		ma=max(ma,w),mi=min(mi,w),ma1=max(ma1,w1),mi1=min(mi1,w1);
	}
	printf("%d",max(ma-mi,ma1-mi1));
	return 0;
}