Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

3
1 1
2 4
3 2

Sample Output 1

4

The Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.

Sample Input 2

2
1 1
1 1

Sample Output 2

0

Solution in C++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include <cstdio>
#ifdef _MSC_VER
#define GC getchar
#else
#define GC getchar_unlocked
#endif
int input()
{
	int x=0;
	char c;
	bool minus=false;
	for(;;)
	{
		c=GC();
		if (c=='-')
		{
			minus=true;
			continue;
		}
		if (c==' '||c=='\n')
			if (minus)
				return -x;
			else
				return x;
		x=10*x+c-'0';
	}
}
void fix()
{
	char c;
	for(;;)
	{
		c=GC();
		if (c==-1||c!=' '&&c!='\n')
			break;
	}
	if (c!=-1)
		ungetc(c,stdin);
}
int main()
{
	int N,i,j,k,d;
	int a[6];
	int m[32];
	int M[32];
	for (i=0; i<32; i++)
	{
		m[i]=1000000000;
		M[i]=-1000000000;
	}
	scanf("%d %d",&N,&d);
	fix();
	for (i=0; i<N; i++)
	{
		for (j=0; j<d; j++)
			a[j]=input();//,fix();
		for (j=0; j<1<<(d-1); j++)
		{
			int x=a[0];
			for (k=0; k<d-1; k++)
				if (j&(1<<k))
					x+=a[k+1];
				else
					x-=a[k+1];
			if (m[j]>x)
				m[j]=x;
			if (M[j]<x)
				M[j]=x;
		}
	}
	int ans=0;
	for (i=0; i<1<<(d-1); i++)
		if (ans<M[i]-m[i])
			ans=M[i]-m[i];
	printf("%d\n",ans);
	return 0;
}