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;

const int INF = 0x3f3f3f3f;
int n, maxn1, maxn2, minn1 = INF, minn2 = INF, x, y;

int main() {
	scanf("%d", &n);
	while (n--) {
		scanf("%d%d", &x, &y);
		y += x;
		if (maxn1 < y) maxn1 = y;
		if (minn1 > y) minn1 = y;
		y -= x * 2;
		if (maxn2 < y) maxn2 = y;
		if (minn2 > y) minn2 = y;
	}
	printf("%d\n", max(maxn1 - minn1, maxn2 - minn2));
	return 0;
}
