Given points in dimensional space, find the minimum "surface area" of a hyperrectangle required to contain all points modulo .
As an example, the "surface area" of a -dimensional hyperrectangle (rectangle) is the sum of its side lengths. The "surface area" of a -dimensional hyperrectangle (rectangular prism) is the sum of the areas of the sides of the hyperrectangle.
Input Specification
The first line will contain two space-separated integers, , the number of dimensions and the number of points respectively.
The next lines will each contain integers, .
Output Specification
Output the minimum "surface area" of a hyperrectangle required to contain all points, modulo .
Subtasks
Subtask 1 [10%]
Subtask 2 [20%]
Subtask 3 [70%]
No additional constraints.
Sample Input 1
2 4
1 1
3 3
-1 2
0 0
Sample Output 1
14
Sample Input 2
5 3
1 4 2 3 4
0 -129 6 9 0
0 0 -10 9 5
Sample Output 2
183436
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