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;
const ll LINF = 1e18;
const int INF = 1e9;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

int main(){
    int N;
    cin>>N;
    int Fp[N],Fm[N];
    rep(i,N){
        int x,y; cin>>x>>y;
        Fm[i]=x-y;
        Fp[i]=x+y;
    }
    sort(Fm,Fm+N);
    sort(Fp,Fp+N);
    cout<<max(Fm[N-1]-Fm[0], Fp[N-1]-Fp[0])<<endl;
    return 0;
}