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>
typedef long long ll;
using namespace std;

ll sa[200010], wa[200010];

int main() {
	int N;
	cin >> N;
	for(int i=0; i<N; ++i){
		ll x, y;
		cin >> x >> y;
		sa[i]=x-y, wa[i]=x+y;
	}
	sort(sa, sa+N);
	sort(wa, wa+N);
	cout << max(sa[N-1]-sa[0], wa[N-1]-wa[0]) << endl;
	return 0;
}