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 target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<cstdint>
#include<cstddef>
#include<algorithm>
#include<vector>
using namespace std;
using i32 = int_fast32_t;
using i64 = int_fast64_t;
using usize = uint_fast64_t;
#define rep(i, n) for (usize i = 0; i < (usize)(n); i++)
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
using P = pair<i64,i64>;

int main(){
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
i32 n;
cin >> n;
vector<P> ab(n);
rep(i,n){
    i64 A,B;
    cin >> A >> B;
    ab[i].first = A - B;
    ab[i].second = A + B;
}
i64 ans = 0;
sort(all(ab));
vector<i64> con(n);
ans = max(ans,ab.back().first - ab.front().first);
rep(i,n){
    swap(ab[i].first,ab[i].second);
}
sort(all(ab));
    ans = max(ans,ab.back().first - ab.front().first);
cout << ans << endl;
}