Little Petya is learning to play chess. He has already learned how to move a king, a rook and a bishop. Let us remind you the rules of moving chess pieces. A chessboard is 64 square fields organized into an 8 × 8 table. A field is represented by a pair of integers (r, c) — the number of the row and the number of the column (in a classical game the columns are traditionally indexed by letters). Each chess piece takes up exactly one field. To make a move is to move a chess piece, the pieces move by the following rules: A rook moves any number of fields horizontally or vertically. A bishop moves any number of fields diagonally. A king moves one field in any direction — horizontally, vertically or diagonally. The pieces move like that Petya is thinking about the following problem: what minimum number of moves is needed for each of these pieces to move from field (r 1, c 1) to field (r 2, c 2)? At that, we assume that there are no more pieces besides this one on the board. Help him solve this problem.

输入描述:

The input contains four integers r1, c1, r2, c2 (1 ≤ r1, c1, r2, c2 ≤ 8) — the coordinates of the starting and the final field. The starting field doesn't coincide with the final one.You can assume that the chessboard rows are numbered from top to bottom 1 through 8, and the columns are numbered from left to right 1 through 8.

输出描述:

Print three space-separated integers: the minimum number of moves the rook, the bishop and the king (in this order) is needed to move from field (r1, c1) to field (r2, c2). If a piece cannot make such a move, print a 0 instead of the corresponding number.