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;

typedef long long ll;

int main(){
  int N; cin >> N;
  vector<ll> P(N);
  vector<ll> Q(N);
  for(int i = 0; i < N; i++){
    ll x,y; cin >> x >> y;
    P[i] = x + y;
    Q[i] = x - y;
  }
  
  sort(P.begin(), P.end());
  sort(Q.begin(), Q.end());
  
  cout << max(abs(P[0] - P[N-1]), abs(Q[0] - Q[N-1]) ) << endl;
}
