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Millenium Leapcow
 Time Limit: 2000MS Memory Limit: 30000K Total Submissions: 2366 Accepted: 868 Case Time Limit: 1000MS

Description

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 square visited by the 'knight' 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.

Input

* Line 1: A single integer: the size of the board

* 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.

Output

* 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'.

Sample Input

```4
1 3 2 16
4 10 6 7
8 11 5 12
9 13 14 15```

Sample Output

```7
2
4
5
9
10
12
13
```

Source

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