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>
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
using namespace std;
int d0[200000],d1[200000];
int main(){
  int N,i,x,y;scanf("%d",&N);
  for(i=0;i<N;i++){
    scanf("%d%d",&x,&y);
    d0[i] = x-y;
    d1[i] = x+y;
  }
  printf("%d\n",max(*max_element(d0,d0+N)-*min_element(d0,d0+N),*max_element(d1,d1+N)-*min_element(d1,d1+N)));
}