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 20000000010ll

long long minx = INF, maxx = -INF, miny = INF, maxy = -INF, x, y, n;

int main()
{
	scanf("%lld", &n);
	for (int i=1; i<=n; i++)
	{
		scanf("%lld%lld", &x, &y);
		minx = min(minx, x + y), maxx = max(maxx, x + y);
        miny = min(miny, x - y), maxy = max(maxy, x - y);
	}
	printf("%lld\n", max(maxx - minx, maxy - miny));
}