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 ("O2")
#pragma GCC target ("avx2")
#include<bits/stdc++.h>

using namespace std;
typedef long long ll;
#define rep(i, n) for(int i = 0; i < (n); i++)
#define rep1(i, n) for(int i = 1; i <= (n); i++)
#define co(x) cout << (x) << "\n"
#define cosp(x) cout << (x) << " "
#define ce(x) cerr << (x) << "\n"
#define cesp(x) cerr << (x) << " "
#define pb push_back
#define mp make_pair
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
#define Would
#define you
#define please


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

	int N;
	cin >> N;

	pair<ll, ll> XY[200001];

	rep(i, N) {
		ll x, y;
		cin >> x >> y;
		XY[i] = mp(x, y);
	}

	sort(XY, XY + N);

	ll ue = XY[0].first + XY[0].second, sita = XY[0].second - XY[0].first;

	ll kotae = 0;
	rep1(i, N - 1) {
		ll x = XY[i].first;
		ll y = XY[i].second;
		chmax(kotae, max(y - ue + x, sita - y + x));

		chmin(ue, x + y);
		chmax(sita, y - x);
	}

	co(kotae);

	Would you please return 0;
}