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 maxn = 1e7 + 10;
const ll mod = 1e9 + 7;
int x[maxn],y[maxn];
int main(){
	int n;
	ll ans;
    cin>>n;
    for(int i = 1;i <= n; i++){
        int a,b;
		cin>>a>>b;
        x[i] = a - b;
        y[i] = a + b;
    }
    sort(x + 1,x + n + 1);
    sort(y + 1,y + n + 1);
    ans = max(x[n] - x[1],y[n] - y[1]);
    cout<<ans<<endl;
    return 0;
}