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>
#define pb push_back
typedef long long ll;
using namespace std;
int main() {
	int n;
	cin >> n;
	int mx1 = -1e9, mx2 = -1e9;
	int mn1 = 2e9, mn2 = 2e9;
	while (n--) {
		int x, y;
		cin >> x >> y;
		mx1 = max(mx1, x + y);
		mx2 = max(mx2, x - y);
		mn1 = min(mn1, x + y);
		mn2 = min(mn2, x - y);
	}
	cout << max(mx1 - mn1, mx2 - mn2) << endl;
}