B"Nauuo is a girl who loves playing chess. One day she invented a game by herself which needs n chess pieces to play on a m x m chessboard. The rows and columns are numbered from 1 to m . We denote a cell on the intersection of the r -th row and c -th column as (r,c) . The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i -th piece lies on (r_i, ,c_i) , while the following rule is satisfied: for all pairs of pieces i and j , |r_i-r_j|+|c_i-c_j| ge|i-j| . Here |x| means the absolute value of x . However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small. She wants to find the smallest chessboard on which she can put n pieces according to the rules. She also wonders how to place the pieces on such a chessboard. Can you help her? The only line contains a single integer n ( 1 <= n <= 1000 ) -- the number of chess pieces for the game. The first line contains a single integer -- the minimum value of m , where m is the length of sides of the suitable chessboard. The i -th of the next n lines contains two integers r_i and c_i ( 1 <= r_i,c_i <= m ) -- the coordinates of the i -th chess piece. If there are multiple answers, print any. In the first example, you can't place the two pieces on a 1 x 1 chessboard without breaking the rule. But you can place two pieces on a 2 x 2 chessboard like this: In the second example, you can't place four pieces on a 2 x 2 chessboard without breaking the rule. For example, if you place the pieces like this: then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1 , |1-3|=2 , 1<2 ; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2 , |1-4|=3 , 2<3 . It doesn't satisfy the rule. However, on a 3 x 3 chessboard, you can place four pieces like this: "...