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>
#define rep(i,n) for (int i = 0; i< (n); i++)
using ll = long long;
using namespace std;

int main(void){
	int N;
	cin >> N;
	vector<pair<ll,int>> v;
	ll x[N], y[N];
	rep(i,N) {
		int p, q;
		cin >> p >> q;
		x[i] = (ll)(p+q);
		y[i] = (ll)(p-q);
	}
	sort(x, x+N);
	sort(y, y+N);
	ll ans = x[N-1] - x[0];
	ans = max(ans, y[N-1] - y[0]);
	cout << ans << endl;
return 0;
}
