The cows have revised their game of leapcow. They now play in the middle of a huge pasture upon which they have marked a grid that bears a remarkable resemblance to a chessboard of N rows and N columns (3 <= N <= 365). Here's how they set up the board for the new leapcow game: * First, the cows obtain N x N squares of paper. They write the integers from 1 through N x N, one number on each piece of paper. * Second, the 'number cow' places the papers on the N x N squares in an order of her choosing. Each of the remaining cows then tries to maximize her score in the game: * First, she chooses a starting square and notes its number. * Then, she makes a 'knight' move (like the knight on a chess board) to a square with a higher number. If she's particularly strong, she leaps to the that square; otherwise she walks. * She continues to make 'knight' moves to higher numbered squares until no more moves are possible. Each 'knight' move earns the competitor a single point. The cow with the most points wins the game. Help the cows figure out the best possible way to play the game.

* Line 1: A single integer: N * Lines 2.....: These lines contain space-separated integers that tell the contents of the chessboard. The first set of lines(starting at the second line of the input file) represents the first row on the chessboard; the next set of lines represents the next row, and so on. To keep the input lines of reasonable length, when N > 15, a row is broken into successive lines of 15 numbers and a potentially shorter line to finish up a row. Each new row begins on its own line.

* Line 1: A single integer that is the winning cow's score; call it W. * Lines 2..W+1: Output, one per line, the integers that are the starting square, the next square the winning cow visits, and so on through the last square. If a winning cow can choose more than one path, show the path that would be the 'smallest' if the paths were sorted by comparing their respective 'square numbers'.

OUTPUT DETAILS: The longest tour consists of the moves 2 to 4, 4 to 5, 5 to 9, 9 to 10, 10 to 12, 12 to 13 and has length of 7 squares.

USACO 2003 U S Open Green Competition