Contest Duration: - (local time) (100 minutes) Back to Home
E - Dist Max /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

ただし、二点 (x_i,y_i)(x_j,y_j) のマンハッタン距離は |x_i-x_j|+|y_i-y_j| のことをいいます。

制約

• 2 \leq N \leq 2 \times 10^5
• 1 \leq x_i,y_i \leq 10^9
• 入力はすべて整数

入力

N
x_1 y_1
x_2 y_2
:
x_N y_N


入力例 1

3
1 1
2 4
3 2


出力例 1

4


1 番目の点と 2 番目の点のマンハッタン距離は |1-2|+|1-4|=4 で、これが最大です。

入力例 2

2
1 1
1 1


出力例 2

0


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


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