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<cstdio>
#include<cmath>
using namespace std;
int n, x, y, a, b, aa, bb, ans;
int main(){
	int i;
	cin >> n >> x >> y;
	a=b=x+y;
	aa=bb=x-y;
	n--;
	while(n--){
		cin >> x >> y;
		a=min(a,x+y);
		b=max(b,x+y);
		aa=min(aa,x-y);
		bb=max(bb,x-y);
	}
	ans=max(b-a,bb-aa);
	cout << ans << endl; 
	return 0;
}