B"A queen is the strongest chess piece. In modern chess the queen can move any number of squares in any horizontal, vertical or diagonal direction (considering that there're no other pieces on its way). The queen combines the options given to the rook and the bishop. There are m queens on a square n xe2 x80 x89 xc3 x97 xe2 x80 x89n chessboard. You know each queen's positions, the i-th queen is positioned in the square (ri, xe2 x80 x89ci), where ri is the board row number (numbered from the top to the bottom from 1 to n), and ci is the board's column number (numbered from the left to the right from 1 to n). No two queens share the same position. For each queen one can count w -- the number of other queens that the given queen threatens (attacks). For a fixed attack direction only the first queen in this direction is under attack if there are many queens are on the ray of the attack. Obviously, for any queen w is between 0 and 8, inclusive. Print the sequence t0, xe2 x80 x89t1, xe2 x80 x89..., xe2 x80 x89t8, where ti is the number of queens that threaten exactly i other queens, i.e. the number of queens that their w equals i. The first line of the input contains a pair of integers n, xe2 x80 x89m (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n, xe2 x80 x89m xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89105), where n is the size of the board and m is the number of queens on the board. Then m following lines contain positions of the queens, one per line. Each line contains a pair of integers ri, xe2 x80 x89ci (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89ri, xe2 x80 x89ci xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n) -- the queen's position. No two queens stand on the same square. Print the required sequence t0, xe2 x80 x89t1, xe2 x80 x89..., xe2 x80 x89t8, separating the numbers with spaces."...