C. Colored Rookstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputIvan is a novice painter. He has n dyes of different colors. He also knows exactly m pairs of colors which harmonize with each other.Ivan also enjoy playing chess. He has 5000 rooks. He wants to take k rooks, paint each of them in one of n colors and then place this k rooks on a chessboard of size 10^{9} \times 10^{9}.Let's call the set of rooks on the board connected if from any rook we can get to any other rook in this set moving only through cells with rooks from this set. Assume that rooks can jump over other rooks, in other words a rook can go to any cell which shares vertical and to any cell which shares horizontal.Ivan wants his arrangement of rooks to have following properties: For any color there is a rook of this color on a board; For any color the set of rooks of this color is connected; For any two different colors a b union of set of rooks of color a and set of rooks of color b is connected if and only if this two colors harmonize with each other.Please help Ivan find such an arrangement.InputThe first line of input contains 2 integers n, m (1 \le n \le 100, 0 \le m \le min(1000, \,\, \frac{n(n-1)}{2})) — number of colors and number of pairs of colors which harmonize with each other.In next m lines pairs of colors which harmonize with each other are listed. Colors are numbered from 1 to n. It is guaranteed that no pair occurs twice in this list.OutputPrint n blocks, i-th of them describes rooks of i-th color.In the first line of block print one number a_{i} (1 \le a_{i} \le 5000) — number of rooks of color i. In each of next a_{i} lines print two integers x and y (1 \le x, \,\, y \le 10^{9}) — coordinates of the next rook.All rooks must be on different cells.Total number of rooks must not exceed 5000.It is guaranteed that the solution exists.ExamplesInput3 21 22 3Output23 41 441 22 22 45 415 1Input3 31 22 33 1Output11 111 211 3Input3 11 3Output11 112 213 1NoteRooks arrangements for all three examples (red is color 1, green is color 2 and blue is color 3).
Input3 21 22 3
Output23 41 441 22 22 45 415 1
['constructive algorithms', 'graphs', '*1700']