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;
typedef long long ll;
int main() {
	int N;
	cin >> N;
	int ma1 = -(1<<30), mi1 = (1<<30);
	int ma2 = -(1<<30), mi2 = (1<<30);
	for (int i = 0; i < N; ++ i) {
		int x, y;
		cin >> x >> y;
		ma1 = max(ma1, x-y);
		mi1 = min(mi1, x-y);
		ma2 = max(ma2, x+y);
		mi2 = min(mi2, x+y);
	}
	cout << max(ma1-mi1, ma2-mi2) << endl;
}
