Life Line

Let's play a new board game, "Life Line".

The number of players is at least 2 and at most 9.

The board is a large regular triangle made of many small regular triangles (Figure 1). Every small triangle has edges of the same length.

Figure 1: The board

The size of the board is the number of vertices on the bottom edge of the outer triangle. For example, the board in Figure 1 has size 4.

At the start of the game, each player receives a distinct identification number between 1 and 9 and some stones with that number written on them.

The players take turns. On a turn, a player puts one of his stones on an empty vertex. An empty vertex is a vertex with no stone on it.

When a player puts a stone on a vertex, some stones may be removed from the board. The player gains one point for each removed stone of another player and loses one point for each removed stone of his own. The points of a player for a turn are the points gained minus the points lost in that turn.

Stones are removed under the following conditions:

The stones on the board are divided into groups. A group is a set of stones that have the same number and are placed adjacently. That is, stones with the same number that are adjacent to each other belong to the same group.
If no stone in a group is adjacent to an empty vertex, all the stones of that group are removed from the board.

Figure 2: Groups of stones

Figure 2 shows an example of groups of stones.

Suppose it is the turn of player '4'. If he puts his stone on the vertex shown in Figure 3a, some groups satisfy the removal condition (shaded in Figure 3b). The player gains 6 points, because 6 stones of other players are removed (Figure 3c).



Figure 3a	Figure 3b	Figure 3c

As another example, suppose it is the turn of player '2' in Figure 2. If he puts his stone on the vertex shown in Figure 4a, some groups satisfy the removal condition (shaded in Figure 4b). The player gains 4 points because 4 stones of other players are removed, but at the same time loses 3 points because 3 of his own stones are removed. The points of this turn are therefore 4 - 3 = 1 (Figure 4c).



Figure 4a	Figure 4b	Figure 4c

The game ends when every player has put all of his stones on the board. The total score of a player is the sum of the points of all his turns.

Write a program that computes the maximum points (points gained minus points lost) the current player can get in his current turn.

The input consists of multiple data sets. Each data set describes the state of a board of a game in progress.

Each data set has the following format.

 N C

          S1,1
       S2,1  S2,2
    S3,1 S3,2 S3,3
          ...
  SN,1    ...    SN,N

$N$ is the size of the board ( $3 \le N \le 10$ ).

$C$ is the identification number of the player whose turn it is ( $1 \le C \le 9$ ). Your program must compute his points for this turn.

$S_{i,j}$ is the state of a vertex of the board ( $0 \le S_{i,j} \le 9$ ). A positive $S_{i,j}$ means that a stone numbered $S_{i,j}$ is on that vertex. A value of 0 means that the vertex is empty. Every board in the input has at least one empty vertex.

A line with two zeros, 0 0, marks the end of the input.

Problem

Input

Output