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;
int main() {
	int n; cin >> n;
	int maxP, minP, maxS, minS;
	maxP = maxS = INT_MIN;
	minP = minS = INT_MAX;
	while (n--) {
		int x, y; cin >> x >> y;
		maxP = max(maxP, x + y);
		minP = min(minP, x + y);
		maxS = max(maxS, x - y);
		minS = min(minS, x - y);
	}
	cout << max(maxP - minP, maxS - minS) << '\n';
    return 0;
}
