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 rep(i, n) for(int i=0; i<n; i++)
typedef int64_t lint;
constexpr lint LINF = LLONG_MAX/2;

int main() {
	int N;
	cin >> N;
	lint a=LINF, b=0, c=LINF, d=0, x, y, z=1000000007;
	rep(i, N) {
		cin >> x >> y;
		a = min(x+y, a);
		b = max(x+y, b);
		c = min(x+(z-y), c);
		d = max(x+(z-y), d);
	}
	std::cout << max(b-a, d-c) << '\n';
}
