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;
#define INF 3000000000

int main(){
	int N;
	cin >> N;
	long long x[N], y[N];
	long long Mp = 0, mp = INF, Mm = -1 * INF, mm = INF;
	for(int i=0;i<N;i++){
		cin >> x[i] >> y[i];
		Mp = max(Mp, x[i] + y[i]);
		mp = min(mp, x[i] + y[i]);
		Mm = max(Mm, x[i] - y[i]);
		mm = min(mm, x[i] - y[i]);
	}
	long long ans = Mp - mp;
	ans = max(ans, Mm - mm);
	cout << ans << endl;
}