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>
#define rep(i, n) for (int i = 0, i##_len = (n); i < i##_len; ++i)
#define reps(i, n) for (int i = 1, i##_len = (n); i <= i##_len; ++i)
#define rrep(i, n) for (int i = ((int)(n)-1); i >= 0; --i)
#define rreps(i, n) for (int i = ((int)(n)); i > 0; --i)
#define rep2(i, s, n) for (int i = (s); i < (int)(n); i++)
#define repc2(i, s, n) for (int i = (s); i <= (int)(n); i++)
// #define inf 2e9
#define linf 9000000000000000000ll
#define all(v) v.begin(), v.end()
using namespace std;
typedef long long ll;

#define N 200009
int n;
vector<pair<ll, ll>> v;
vector<ll> vx, vy;
ll f1(ll x, ll y) {
    return x - y;
}
ll f2(ll x, ll y) {
    return x + y;
}

int main() {
    cin >> n;
    v.resize(n);
    vx.resize(n);
    vy.resize(n);
    rep(i, n) {
        scanf("%lld%lld", &v[i].first, &v[i].second);
        vx[i] = v[i].first - v[i].second;
        vy[i] = v[i].first + v[i].second;
    }
    ll ans = 0;
    ll vxmax = *max_element(all(vx));
    ll vymax = *max_element(all(vy));
    ll vxmin = *min_element(all(vx));
    ll vymin = *min_element(all(vy));
    reps(i, n) {
        ans = max(ans, vxmax - vxmin);
        ans = max(ans, vymax - vymin);
    }

    cout << ans << endl;
    return 0;
}