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;

const int mod = 1e9;
int main()
{
	int N;
	scanf("%d",&N);
	
	int Max1 = mod*-1,Min1 = mod;
	int Max0 = mod*-1,Min0 = mod;
	for(int i = 1;i <= N;++i)
	{
		int x,y;
		scanf("%d%d",&x,&y);
		
		Max1 = max(Max1,x+y);
		Min1 = min(Min1,x+y);
		Max0 = max(Max0,x-y);
		Min0 = min(Min0,x-y); 
	}
	int ans = max((Max1 - Min1) , (Max0 - Min0));
	return printf("%d",ans),0;
} 