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;
using ll=long long int;
ll mod=1e9+7;
int main()
{
    ll n;
    cin>>n;
    vector<ll>  a(n);
    vector<ll> b(n);
    for(ll i=0;i<n;i++)
    {
        ll x,y;
        cin>>x>>y;
        a[i]=x+y;
        b[i]=x-y;
    }
    sort(begin(a),end(a));
    sort(begin(b),end(b));
    cout<<max(abs(a[n-1]-a[0]),abs(b[n-1]-b[0]))<<endl;
}
