Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

3
1 1
2 4
3 2

Sample Output 1

4

The Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.

Sample Input 2

2
1 1
1 1

Sample Output 2

0

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define ull unsigned long long
#define mii make_pair<int, int>
#define mll make_pair<ll, ll>
#define pii pair<int, int>
#define pll pair<ll, ll>
#define vi vector<int>
#define vvi vector<vector<int>>
#define vl vector<ll>
#define vvl vector<vector<ll>>
#define vb vector<bool>
#define vvb vector<vector<bool>>
#define vc vector<char>
#define vvc vector<vector<char>>
#define all(v) (v).begin(), (v).end()

//ofstream out("debug.txt");

const int MxN = 1e5, md = 1e9 + 7;

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    int n;
    cin >> n;
    vl x(n), y(n);
    for (int i = 0; i < n; ++i)
        cin >> x[i] >> y[i];
    ll ans = 0, mi, cur;
    for (ll a : {1, -1})
        for (ll b : {1, -1})
        {
            mi = a * x[0] + b * y[0];
            for (ll i = 1; i < n; ++i)
            {
                cur = a * x[i] + b * y[i];
                ans = max(ans, cur - mi);
                mi = min(mi, cur);
            }
        }
    cout << ans << '\n';
}