- This problem has no input files.

Alice entered a local chess tournament where she will play Bob a total of seven times, wielding white pieces every time. Bob is not a very good chess player and he is notorious for using a lazy strategy. He always mirrors his opponent’s moves. For example, when Alice starts by moving her pawn `e2`

to `e4`

(denoted `1. e4`

in Standard Algebraic Notation), Bob will respond by moving his pawn from `e7`

to `e5`

(`1. ... e5`

). When she follows with a queen move `2. Qh5`

, he will counter with `2. ... Qh4`

. Of course, such a mirroring move is not always possible. For example, if after the said two moves Alice captures the queen by playing `3. Qxh4`

, Bob can no longer reply the same way, as he has no queen left. Similarly, if Alice played `3. Qxf7+`

, Bob would be in check and the move `3. ... Qxf2+`

would be illegal. When such a situation occurs, Bob will just stare at the chessboard until his time runs out.

Alice considers games with Bob a waste of time, so she wants to win them as fast as possible. This means that the number of moves has to be as small as possible, and Bob has to be able to mirror her every move until the move that delivers the checkmate.

However, Alice wants to challenge herself at least a little bit. She wants to play seven different games, and in each of them use a different piece in the move that delivers the checkmate. That is, there has to be a game where the last move is performed by a pawn, a knight, a bishop, a rook, a queen, a king, and any promoted piece, respectively. Your task is to suggest such games to Alice.

Note that the piece considered to deliver the mate is the one that moves in Alice’s last turn, even if it’s just moving out of the way (a discovered attack). Delivering the mate with a promoted piece counts as a promoted piece victory regardless of whether you promoted it to a queen, a rook, a bishop or a knight. When the promotion itself is a checkmate, it is considered to be a promoted piece move and not a pawn move. Castling is considered to be a king move, not a rook move.

Submit a valid file in Portable Game Notation (PGN) containing at most 7 games. We will ignore all comments, tags, and variations (but they still have to be syntactically correct if present) and only consider the main line. So the simplest way is to submit a file containing **only the movetext for each game**, separated by blank lines.

Each game has to be valid and follow the above rules. It has to be legal, end with the black king in a checkmate, and every black move has to mirror the immediately previous white move.

For each piece type you can score a point. In order to determine whether you do, we count the number of moves in your shortest game (defaulting to 100 if no game of that type has been submitted) and then we do the same for our best solution. To score a point, your solution has to use at most as many moves as ours.

In the **easy subproblem L1** you need to score at least 3 points.

In the **hard subproblem L2** you need the full 7 points.

Below is an example of a file you might submit. The file contains four consecutive games in PGN, separated by a blank line.

```
1. f3 e5
2. g4?? Qh4#
1. e4 e5 2. Bc4 Bc5 3. Qh5 Nf6 4. Qxf7#
1.c3 c6 2.Qc2 Qc7 3.Qxh7 Qxh2 4.g3 g6 5.Bg2 Bg7 6.Qxg7 Qxg2 7.Qxh8 Qxh1 8.Qxg8#
[FEN "8/3RP2k/6pp/3N4/3n4/8/3rp2K/8 w - - 0 1"]
[SetUp "1"]
1.e8=Q#
```

This submit would get a Wrong answer for the following reasons:

The first example game is incorrect because it ends with white king in checkmate.

The second example game is incorrect because the black’s third move is not a mirror image of the third white’s move.

The third game is correct. However, you will not get a point because there is a better solution for the queen giving the checkmate.

The fourth game is incorrect as you didn’t use the standard starting position. Note that the mating move would be only considered a checkmate by a promoted piece for the purposes of this task, and not pawn, queen or rook.