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;
    ll mn = 1e18, mnn = 1e18;
    ll mx = -1e18, mxx = -1e18;
    while (n--)
    {
        ll x, y;
        cin >> x >> y;
        mn = min(mn, x + y);
        mx = max(mx, x + y);
        mnn = min(mnn, x - y);
        mxx = max(mxx, x - y);
    }
    cout << max(mx - mn, mxx - mnn);
}