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문제

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 (R1C1) and (R2C2) 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.

입력

The input contains five integers in a line: N R1 R2 C1 C2 (1 ≤ N ≤ 1,000,000,000; 1 ≤ R1 ≤ R2N; 1 ≤ C1 ≤ C2N) as stated in the problem description.

출력

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

예제 입력 1

5 3 3 3 3

예제 출력 1

1

예제 입력 2

5 1 5 1 5

예제 출력 2

325

예제 입력 3

5 4 5 4 5

예제 출력 3

70

예제 입력 4

1 1 1 1 1

예제 출력 4

1