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)

#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math,O3")

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

typedef unsigned long long int ull;
typedef long long ll;
#define pb push_back

int main()
{
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    //your code starts here
    int n;
    cin >> n;
    ll diff[4][n];
    for (int i = 0; i < n; i++)
    {
        ll x, y;
        cin >> x >> y;
        diff[0][i] = x + y;
        diff[1][i] = x - y;
        diff[2][i] = -diff[1][i];
        diff[3][i] = -diff[0][i];
    }
    for (int i = 0; i < 4; i++)
        sort(diff[i], diff[i] + n);
    ll ans = INT_MIN;
    for (int i = 0; i < 4; i++)
        ans = max(ans, diff[i][n - 1] - diff[i][0]);
    cout << ans << "\n";
    return 0;
}