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.

Examples

Input

3
1 1
2 4
3 2


Output

4


Input

2
1 1
1 1


Output

0
#include "bits/stdc++.h"
using namespace std;

#define ll long long
#define rep(i,n) for(int i = 0;i < (n); i++)
#define mod 1000000007

int main() {
	ll n;
	cin >> n;
	ll x, y;
	ll ans;
	vector<ll> a(n);
	vector<ll> b(n);
	rep(i, n) {
		cin >> x >> y;
		a[i] = x + y;
		b[i] = x - y;
	}
	sort(a.begin(), a.end());
	sort(b.begin(), b.end());
	ans = max(a[n - 1] - a[0], b[n - 1] - b[0]);
	cout << ans << endl;
	return 0;
}