21046번 - Pretty Table 다국어

A pretty table is a grid with N rows and N columns containing integers from 1 to N². The numbers are written on the grid following these rules:

• At first, 1 is written in the center cell, i.e. the cell on the (N/2+1)-th row and ((N/2+1)-th column, where / is the integer division (i.e. rounded down since N/2 here is always positive).
• Then, starting from the cell on the left of the cell containing integer 1, in clockwise direction, continues writing the integers 2 to N² one by one, surrounding the existing numbers.

For example, if N = 5, the table will look like this:

Given N, R₁, R₂, C₁, and C₂, calculates the sum of the integers contained within the sub-grid having (R₁, C₁) and (R2, C₂) as the top-left-most cell and the bottom-right-most cell. Note that the table index starts from 1 to N on both row and column.

The input contains five integers in a line: N R₁ R₂ C₁ C₂ (1 ≤ N ≤ 1,000,000,000; 1 ≤ R₁ ≤ R₂ ≤ N; 1 ≤ C₁ ≤ C₂ ≤ N) as stated in the problem description.

The output contains the remainder of the answer when divided by 1,000,000,007, in a line.