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;

#define ll long long
#define pii pair<int,int>
#define mod 1000000007
int main()
{
    int n;
    cin>>n;
    vector<ll> a(n),b(n);
    ll x,y;
    for(int i=0;i<n;i++)
    {
        cin>>x>>y;
        a[i] = x+y;
        b[i] = x-y;
    }
    sort(a.begin(),a.end());
    sort(b.begin(),b.end());
    ll nax = max(a[n-1] -a[0],b[n-1]-b[0]);
    cout<<nax<<endl;
}