カードゲームを作っているので、事前にカードを作成してmysqlテーブルに保存する必要があります。私はそれらを作成するためのphpスクリプトを作成する方法を理解しようとしています。さて、0から12まで変化する値の6つのカテゴリがあり、すべてのカードには各カテゴリの値があります。各カードのカテゴリの値の合計は36でなければなりません。したがって、各カードは次のようになります。
また
あるいは
50枚か60枚のカードをランダムに生成できれば素晴らしいと思います。
前もって感謝します。
このようなものは機能するはずです-ロジックが少しずれている可能性があります、私はそれをテストしていません。
function generate_card() {
$max_card = 12; // What's the highest value of a card number?
$min_card = 0; // What's the lowest value of a card number?
$num_cards = 6; // How many numbers on a card?
$total = 36; // What's the desired sum?
$numbers = array();
$running_total = 0;
for ($i = 0; $i < $num_cards; ++$i) {
$max = min($max_card, $total - $running_total); //The highest number we can choose
$min = max($min_card, $total - $running_total - ($max_card * ($num_cards - ($i + 1)))); //The lowest number we can choose
//- how much is left ? $total - $running total
//- min is amount_left - ($max_card
$number = rand($min, $max);
$running_total += $number;
$numbers[] = $number;
}
return $numbers;
}
編集：括弧とインデックスを置き忘れましたが、正しく機能するようになりました。
本当に素朴なアプローチは次のとおりです。
/* return an array of 6 numbers between 0 and 12 that sum to 36 */
generate_card() {
$numbers = array();
for($i = 0; $i < 6; $i += 1) {
$numbers[$i] = rand(0, 12);
}
if (array_sum($numbers) !== 36) {
return generate_card(); // repeat until we find one that does sum to 36
} else {
return $numbers; // yay!
}
}
これは「シンプルなカードゲーム」には十分に機能すると思います。
あなたがすでにこれに対する答えを選んだことは知っていますが、それがテーブルに何かをもたらすと思うので、とにかく私の解決策を検討すると思いました。
問題の一部は、「ランダムな手」が意味するものがここではやや曖昧であるということです。合計が36になる6枚のカードの真にランダムなハンドが必要な場合は、合計が36になる可能性のあるすべてのハンドから同じ確率で選ぶ必要があります。
数値を合計できる方法の数は、パーティショニングと呼ばれます。36の可能なすべてのパーティションを生成するアルゴリズムを作成しました。これは17,000個のパーティションです。次に、12を超える数を使用するパーティションを削除し、次に6を超える数を使用するパーティションを削除しました。それは私に6枚のカードの676の可能な手で合計36を残しました。
完全なランダム性を確保するために私が取るアプローチは、すべての可能な手の配列からランダムに選ぶことです。これはストレージを大量に消費しますが（配列を格納する必要があります）、提案されているどのアプローチよりもはるかに高速です（乱数を1つだけ選択してから、配列から取り出すため）。省略されたコードは次のとおりです（続く完全なコード）：
$allHands = array(
array(12,12,12,0,0,0),
array(12,12,11,1,0,0),
array(12,12,10,2,0,0),
array(12,12,10,1,1,0),
// ...etc
);
$hand = $allHands[ rand( 0, count($allHands)-1 ) ];
shuffle( $hand );
// $hand is now a completely random hand of 6 cards summing to 36
考えられるすべてのハンドの完全な配列は次のとおりです。
$allHands = array(
array( 12, 12, 12, 0, 0, 0 ),
array( 12, 12, 11, 1, 0, 0 ),
array( 12, 12, 10, 2, 0, 0 ),
array( 12, 12, 10, 1, 1, 0 ),
array( 12, 12, 9, 3, 0, 0 ),
array( 12, 12, 9, 2, 1, 0 ),
array( 12, 12, 9, 1, 1, 1 ),
array( 12, 12, 8, 4, 0, 0 ),
array( 12, 12, 8, 3, 1, 0 ),
array( 12, 12, 8, 2, 2, 0 ),
array( 12, 12, 8, 2, 1, 1 ),
array( 12, 12, 7, 5, 0, 0 ),
array( 12, 12, 7, 4, 1, 0 ),
array( 12, 12, 7, 3, 2, 0 ),
array( 12, 12, 7, 3, 1, 1 ),
array( 12, 12, 7, 2, 2, 1 ),
array( 12, 12, 6, 6, 0, 0 ),
array( 12, 12, 6, 5, 1, 0 ),
array( 12, 12, 6, 4, 2, 0 ),
array( 12, 12, 6, 4, 1, 1 ),
array( 12, 12, 6, 3, 3, 0 ),
array( 12, 12, 6, 3, 2, 1 ),
array( 12, 12, 6, 2, 2, 2 ),
array( 12, 12, 5, 5, 2, 0 ),
array( 12, 12, 5, 5, 1, 1 ),
array( 12, 12, 5, 4, 3, 0 ),
array( 12, 12, 5, 4, 2, 1 ),
array( 12, 12, 5, 3, 3, 1 ),
array( 12, 12, 5, 3, 2, 2 ),
array( 12, 12, 4, 4, 4, 0 ),
array( 12, 12, 4, 4, 3, 1 ),
array( 12, 12, 4, 4, 2, 2 ),
array( 12, 12, 4, 3, 3, 2 ),
array( 12, 12, 3, 3, 3, 3 ),
array( 12, 11, 11, 2, 0, 0 ),
array( 12, 11, 11, 1, 1, 0 ),
array( 12, 11, 10, 3, 0, 0 ),
array( 12, 11, 10, 2, 1, 0 ),
array( 12, 11, 10, 1, 1, 1 ),
array( 12, 11, 9, 4, 0, 0 ),
array( 12, 11, 9, 3, 1, 0 ),
array( 12, 11, 9, 2, 2, 0 ),
array( 12, 11, 9, 2, 1, 1 ),
array( 12, 11, 8, 5, 0, 0 ),
array( 12, 11, 8, 4, 1, 0 ),
array( 12, 11, 8, 3, 2, 0 ),
array( 12, 11, 8, 3, 1, 1 ),
array( 12, 11, 8, 2, 2, 1 ),
array( 12, 11, 7, 6, 0, 0 ),
array( 12, 11, 7, 5, 1, 0 ),
array( 12, 11, 7, 4, 2, 0 ),
array( 12, 11, 7, 4, 1, 1 ),
array( 12, 11, 7, 3, 3, 0 ),
array( 12, 11, 7, 3, 2, 1 ),
array( 12, 11, 7, 2, 2, 2 ),
array( 12, 11, 6, 6, 1, 0 ),
array( 12, 11, 6, 5, 2, 0 ),
array( 12, 11, 6, 5, 1, 1 ),
array( 12, 11, 6, 4, 3, 0 ),
array( 12, 11, 6, 4, 2, 1 ),
array( 12, 11, 6, 3, 3, 1 ),
array( 12, 11, 6, 3, 2, 2 ),
array( 12, 11, 5, 5, 3, 0 ),
array( 12, 11, 5, 5, 2, 1 ),
array( 12, 11, 5, 4, 4, 0 ),
array( 12, 11, 5, 4, 3, 1 ),
array( 12, 11, 5, 4, 2, 2 ),
array( 12, 11, 5, 3, 3, 2 ),
array( 12, 11, 4, 4, 4, 1 ),
array( 12, 11, 4, 4, 3, 2 ),
array( 12, 11, 4, 3, 3, 3 ),
array( 12, 10, 10, 4, 0, 0 ),
array( 12, 10, 10, 3, 1, 0 ),
array( 12, 10, 10, 2, 2, 0 ),
array( 12, 10, 10, 2, 1, 1 ),
array( 12, 10, 9, 5, 0, 0 ),
array( 12, 10, 9, 4, 1, 0 ),
array( 12, 10, 9, 3, 2, 0 ),
array( 12, 10, 9, 3, 1, 1 ),
array( 12, 10, 9, 2, 2, 1 ),
array( 12, 10, 8, 6, 0, 0 ),
array( 12, 10, 8, 5, 1, 0 ),
array( 12, 10, 8, 4, 2, 0 ),
array( 12, 10, 8, 4, 1, 1 ),
array( 12, 10, 8, 3, 3, 0 ),
array( 12, 10, 8, 3, 2, 1 ),
array( 12, 10, 8, 2, 2, 2 ),
array( 12, 10, 7, 7, 0, 0 ),
array( 12, 10, 7, 6, 1, 0 ),
array( 12, 10, 7, 5, 2, 0 ),
array( 12, 10, 7, 5, 1, 1 ),
array( 12, 10, 7, 4, 3, 0 ),
array( 12, 10, 7, 4, 2, 1 ),
array( 12, 10, 7, 3, 3, 1 ),
array( 12, 10, 7, 3, 2, 2 ),
array( 12, 10, 6, 6, 2, 0 ),
array( 12, 10, 6, 6, 1, 1 ),
array( 12, 10, 6, 5, 3, 0 ),
array( 12, 10, 6, 5, 2, 1 ),
array( 12, 10, 6, 4, 4, 0 ),
array( 12, 10, 6, 4, 3, 1 ),
array( 12, 10, 6, 4, 2, 2 ),
array( 12, 10, 6, 3, 3, 2 ),
array( 12, 10, 5, 5, 4, 0 ),
array( 12, 10, 5, 5, 3, 1 ),
array( 12, 10, 5, 5, 2, 2 ),
array( 12, 10, 5, 4, 4, 1 ),
array( 12, 10, 5, 4, 3, 2 ),
array( 12, 10, 5, 3, 3, 3 ),
array( 12, 10, 4, 4, 4, 2 ),
array( 12, 10, 4, 4, 3, 3 ),
array( 12, 9, 9, 6, 0, 0 ),
array( 12, 9, 9, 5, 1, 0 ),
array( 12, 9, 9, 4, 2, 0 ),
array( 12, 9, 9, 4, 1, 1 ),
array( 12, 9, 9, 3, 3, 0 ),
array( 12, 9, 9, 3, 2, 1 ),
array( 12, 9, 9, 2, 2, 2 ),
array( 12, 9, 8, 7, 0, 0 ),
array( 12, 9, 8, 6, 1, 0 ),
array( 12, 9, 8, 5, 2, 0 ),
array( 12, 9, 8, 5, 1, 1 ),
array( 12, 9, 8, 4, 3, 0 ),
array( 12, 9, 8, 4, 2, 1 ),
array( 12, 9, 8, 3, 3, 1 ),
array( 12, 9, 8, 3, 2, 2 ),
array( 12, 9, 7, 7, 1, 0 ),
array( 12, 9, 7, 6, 2, 0 ),
array( 12, 9, 7, 6, 1, 1 ),
array( 12, 9, 7, 5, 3, 0 ),
array( 12, 9, 7, 5, 2, 1 ),
array( 12, 9, 7, 4, 4, 0 ),
array( 12, 9, 7, 4, 3, 1 ),
array( 12, 9, 7, 4, 2, 2 ),
array( 12, 9, 7, 3, 3, 2 ),
array( 12, 9, 6, 6, 3, 0 ),
array( 12, 9, 6, 6, 2, 1 ),
array( 12, 9, 6, 5, 4, 0 ),
array( 12, 9, 6, 5, 3, 1 ),
array( 12, 9, 6, 5, 2, 2 ),
array( 12, 9, 6, 4, 4, 1 ),
array( 12, 9, 6, 4, 3, 2 ),
array( 12, 9, 6, 3, 3, 3 ),
array( 12, 9, 5, 5, 5, 0 ),
array( 12, 9, 5, 5, 4, 1 ),
array( 12, 9, 5, 5, 3, 2 ),
array( 12, 9, 5, 4, 4, 2 ),
array( 12, 9, 5, 4, 3, 3 ),
array( 12, 9, 4, 4, 4, 3 ),
array( 12, 8, 8, 8, 0, 0 ),
array( 12, 8, 8, 7, 1, 0 ),
array( 12, 8, 8, 6, 2, 0 ),
array( 12, 8, 8, 6, 1, 1 ),
array( 12, 8, 8, 5, 3, 0 ),
array( 12, 8, 8, 5, 2, 1 ),
array( 12, 8, 8, 4, 4, 0 ),
array( 12, 8, 8, 4, 3, 1 ),
array( 12, 8, 8, 4, 2, 2 ),
array( 12, 8, 8, 3, 3, 2 ),
array( 12, 8, 7, 7, 2, 0 ),
array( 12, 8, 7, 7, 1, 1 ),
array( 12, 8, 7, 6, 3, 0 ),
array( 12, 8, 7, 6, 2, 1 ),
array( 12, 8, 7, 5, 4, 0 ),
array( 12, 8, 7, 5, 3, 1 ),
array( 12, 8, 7, 5, 2, 2 ),
array( 12, 8, 7, 4, 4, 1 ),
array( 12, 8, 7, 4, 3, 2 ),
array( 12, 8, 7, 3, 3, 3 ),
array( 12, 8, 6, 6, 4, 0 ),
array( 12, 8, 6, 6, 3, 1 ),
array( 12, 8, 6, 6, 2, 2 ),
array( 12, 8, 6, 5, 5, 0 ),
array( 12, 8, 6, 5, 4, 1 ),
array( 12, 8, 6, 5, 3, 2 ),
array( 12, 8, 6, 4, 4, 2 ),
array( 12, 8, 6, 4, 3, 3 ),
array( 12, 8, 5, 5, 5, 1 ),
array( 12, 8, 5, 5, 4, 2 ),
array( 12, 8, 5, 5, 3, 3 ),
array( 12, 8, 5, 4, 4, 3 ),
array( 12, 8, 4, 4, 4, 4 ),
array( 12, 7, 7, 7, 3, 0 ),
array( 12, 7, 7, 7, 2, 1 ),
array( 12, 7, 7, 6, 4, 0 ),
array( 12, 7, 7, 6, 3, 1 ),
array( 12, 7, 7, 6, 2, 2 ),
array( 12, 7, 7, 5, 5, 0 ),
array( 12, 7, 7, 5, 4, 1 ),
array( 12, 7, 7, 5, 3, 2 ),
array( 12, 7, 7, 4, 4, 2 ),
array( 12, 7, 7, 4, 3, 3 ),
array( 12, 7, 6, 6, 5, 0 ),
array( 12, 7, 6, 6, 4, 1 ),
array( 12, 7, 6, 6, 3, 2 ),
array( 12, 7, 6, 5, 5, 1 ),
array( 12, 7, 6, 5, 4, 2 ),
array( 12, 7, 6, 5, 3, 3 ),
array( 12, 7, 6, 4, 4, 3 ),
array( 12, 7, 5, 5, 5, 2 ),
array( 12, 7, 5, 5, 4, 3 ),
array( 12, 7, 5, 4, 4, 4 ),
array( 12, 6, 6, 6, 6, 0 ),
array( 12, 6, 6, 6, 5, 1 ),
array( 12, 6, 6, 6, 4, 2 ),
array( 12, 6, 6, 6, 3, 3 ),
array( 12, 6, 6, 5, 5, 2 ),
array( 12, 6, 6, 5, 4, 3 ),
array( 12, 6, 6, 4, 4, 4 ),
array( 12, 6, 5, 5, 5, 3 ),
array( 12, 6, 5, 5, 4, 4 ),
array( 12, 5, 5, 5, 5, 4 ),
array( 11, 11, 11, 3, 0, 0 ),
array( 11, 11, 11, 2, 1, 0 ),
array( 11, 11, 11, 1, 1, 1 ),
array( 11, 11, 10, 4, 0, 0 ),
array( 11, 11, 10, 3, 1, 0 ),
array( 11, 11, 10, 2, 2, 0 ),
array( 11, 11, 10, 2, 1, 1 ),
array( 11, 11, 9, 5, 0, 0 ),
array( 11, 11, 9, 4, 1, 0 ),
array( 11, 11, 9, 3, 2, 0 ),
array( 11, 11, 9, 3, 1, 1 ),
array( 11, 11, 9, 2, 2, 1 ),
array( 11, 11, 8, 6, 0, 0 ),
array( 11, 11, 8, 5, 1, 0 ),
array( 11, 11, 8, 4, 2, 0 ),
array( 11, 11, 8, 4, 1, 1 ),
array( 11, 11, 8, 3, 3, 0 ),
array( 11, 11, 8, 3, 2, 1 ),
array( 11, 11, 8, 2, 2, 2 ),
array( 11, 11, 7, 7, 0, 0 ),
array( 11, 11, 7, 6, 1, 0 ),
array( 11, 11, 7, 5, 2, 0 ),
array( 11, 11, 7, 5, 1, 1 ),
array( 11, 11, 7, 4, 3, 0 ),
array( 11, 11, 7, 4, 2, 1 ),
array( 11, 11, 7, 3, 3, 1 ),
array( 11, 11, 7, 3, 2, 2 ),
array( 11, 11, 6, 6, 2, 0 ),
array( 11, 11, 6, 6, 1, 1 ),
array( 11, 11, 6, 5, 3, 0 ),
array( 11, 11, 6, 5, 2, 1 ),
array( 11, 11, 6, 4, 4, 0 ),
array( 11, 11, 6, 4, 3, 1 ),
array( 11, 11, 6, 4, 2, 2 ),
array( 11, 11, 6, 3, 3, 2 ),
array( 11, 11, 5, 5, 4, 0 ),
array( 11, 11, 5, 5, 3, 1 ),
array( 11, 11, 5, 5, 2, 2 ),
array( 11, 11, 5, 4, 4, 1 ),
array( 11, 11, 5, 4, 3, 2 ),
array( 11, 11, 5, 3, 3, 3 ),
array( 11, 11, 4, 4, 4, 2 ),
array( 11, 11, 4, 4, 3, 3 ),
array( 11, 10, 10, 5, 0, 0 ),
array( 11, 10, 10, 4, 1, 0 ),
array( 11, 10, 10, 3, 2, 0 ),
array( 11, 10, 10, 3, 1, 1 ),
array( 11, 10, 10, 2, 2, 1 ),
array( 11, 10, 9, 6, 0, 0 ),
array( 11, 10, 9, 5, 1, 0 ),
array( 11, 10, 9, 4, 2, 0 ),
array( 11, 10, 9, 4, 1, 1 ),
array( 11, 10, 9, 3, 3, 0 ),
array( 11, 10, 9, 3, 2, 1 ),
array( 11, 10, 9, 2, 2, 2 ),
array( 11, 10, 8, 7, 0, 0 ),
array( 11, 10, 8, 6, 1, 0 ),
array( 11, 10, 8, 5, 2, 0 ),
array( 11, 10, 8, 5, 1, 1 ),
array( 11, 10, 8, 4, 3, 0 ),
array( 11, 10, 8, 4, 2, 1 ),
array( 11, 10, 8, 3, 3, 1 ),
array( 11, 10, 8, 3, 2, 2 ),
array( 11, 10, 7, 7, 1, 0 ),
array( 11, 10, 7, 6, 2, 0 ),
array( 11, 10, 7, 6, 1, 1 ),
array( 11, 10, 7, 5, 3, 0 ),
array( 11, 10, 7, 5, 2, 1 ),
array( 11, 10, 7, 4, 4, 0 ),
array( 11, 10, 7, 4, 3, 1 ),
array( 11, 10, 7, 4, 2, 2 ),
array( 11, 10, 7, 3, 3, 2 ),
array( 11, 10, 6, 6, 3, 0 ),
array( 11, 10, 6, 6, 2, 1 ),
array( 11, 10, 6, 5, 4, 0 ),
array( 11, 10, 6, 5, 3, 1 ),
array( 11, 10, 6, 5, 2, 2 ),
array( 11, 10, 6, 4, 4, 1 ),
array( 11, 10, 6, 4, 3, 2 ),
array( 11, 10, 6, 3, 3, 3 ),
array( 11, 10, 5, 5, 5, 0 ),
array( 11, 10, 5, 5, 4, 1 ),
array( 11, 10, 5, 5, 3, 2 ),
array( 11, 10, 5, 4, 4, 2 ),
array( 11, 10, 5, 4, 3, 3 ),
array( 11, 10, 4, 4, 4, 3 ),
array( 11, 9, 9, 7, 0, 0 ),
array( 11, 9, 9, 6, 1, 0 ),
array( 11, 9, 9, 5, 2, 0 ),
array( 11, 9, 9, 5, 1, 1 ),
array( 11, 9, 9, 4, 3, 0 ),
array( 11, 9, 9, 4, 2, 1 ),
array( 11, 9, 9, 3, 3, 1 ),
array( 11, 9, 9, 3, 2, 2 ),
array( 11, 9, 8, 8, 0, 0 ),
array( 11, 9, 8, 7, 1, 0 ),
array( 11, 9, 8, 6, 2, 0 ),
array( 11, 9, 8, 6, 1, 1 ),
array( 11, 9, 8, 5, 3, 0 ),
array( 11, 9, 8, 5, 2, 1 ),
array( 11, 9, 8, 4, 4, 0 ),
array( 11, 9, 8, 4, 3, 1 ),
array( 11, 9, 8, 4, 2, 2 ),
array( 11, 9, 8, 3, 3, 2 ),
array( 11, 9, 7, 7, 2, 0 ),
array( 11, 9, 7, 7, 1, 1 ),
array( 11, 9, 7, 6, 3, 0 ),
array( 11, 9, 7, 6, 2, 1 ),
array( 11, 9, 7, 5, 4, 0 ),
array( 11, 9, 7, 5, 3, 1 ),
array( 11, 9, 7, 5, 2, 2 ),
array( 11, 9, 7, 4, 4, 1 ),
array( 11, 9, 7, 4, 3, 2 ),
array( 11, 9, 7, 3, 3, 3 ),
array( 11, 9, 6, 6, 4, 0 ),
array( 11, 9, 6, 6, 3, 1 ),
array( 11, 9, 6, 6, 2, 2 ),
array( 11, 9, 6, 5, 5, 0 ),
array( 11, 9, 6, 5, 4, 1 ),
array( 11, 9, 6, 5, 3, 2 ),
array( 11, 9, 6, 4, 4, 2 ),
array( 11, 9, 6, 4, 3, 3 ),
array( 11, 9, 5, 5, 5, 1 ),
array( 11, 9, 5, 5, 4, 2 ),
array( 11, 9, 5, 5, 3, 3 ),
array( 11, 9, 5, 4, 4, 3 ),
array( 11, 9, 4, 4, 4, 4 ),
array( 11, 8, 8, 8, 1, 0 ),
array( 11, 8, 8, 7, 2, 0 ),
array( 11, 8, 8, 7, 1, 1 ),
array( 11, 8, 8, 6, 3, 0 ),
array( 11, 8, 8, 6, 2, 1 ),
array( 11, 8, 8, 5, 4, 0 ),
array( 11, 8, 8, 5, 3, 1 ),
array( 11, 8, 8, 5, 2, 2 ),
array( 11, 8, 8, 4, 4, 1 ),
array( 11, 8, 8, 4, 3, 2 ),
array( 11, 8, 8, 3, 3, 3 ),
array( 11, 8, 7, 7, 3, 0 ),
array( 11, 8, 7, 7, 2, 1 ),
array( 11, 8, 7, 6, 4, 0 ),
array( 11, 8, 7, 6, 3, 1 ),
array( 11, 8, 7, 6, 2, 2 ),
array( 11, 8, 7, 5, 5, 0 ),
array( 11, 8, 7, 5, 4, 1 ),
array( 11, 8, 7, 5, 3, 2 ),
array( 11, 8, 7, 4, 4, 2 ),
array( 11, 8, 7, 4, 3, 3 ),
array( 11, 8, 6, 6, 5, 0 ),
array( 11, 8, 6, 6, 4, 1 ),
array( 11, 8, 6, 6, 3, 2 ),
array( 11, 8, 6, 5, 5, 1 ),
array( 11, 8, 6, 5, 4, 2 ),
array( 11, 8, 6, 5, 3, 3 ),
array( 11, 8, 6, 4, 4, 3 ),
array( 11, 8, 5, 5, 5, 2 ),
array( 11, 8, 5, 5, 4, 3 ),
array( 11, 8, 5, 4, 4, 4 ),
array( 11, 7, 7, 7, 4, 0 ),
array( 11, 7, 7, 7, 3, 1 ),
array( 11, 7, 7, 7, 2, 2 ),
array( 11, 7, 7, 6, 5, 0 ),
array( 11, 7, 7, 6, 4, 1 ),
array( 11, 7, 7, 6, 3, 2 ),
array( 11, 7, 7, 5, 5, 1 ),
array( 11, 7, 7, 5, 4, 2 ),
array( 11, 7, 7, 5, 3, 3 ),
array( 11, 7, 7, 4, 4, 3 ),
array( 11, 7, 6, 6, 6, 0 ),
array( 11, 7, 6, 6, 5, 1 ),
array( 11, 7, 6, 6, 4, 2 ),
array( 11, 7, 6, 6, 3, 3 ),
array( 11, 7, 6, 5, 5, 2 ),
array( 11, 7, 6, 5, 4, 3 ),
array( 11, 7, 6, 4, 4, 4 ),
array( 11, 7, 5, 5, 5, 3 ),
array( 11, 7, 5, 5, 4, 4 ),
array( 11, 6, 6, 6, 6, 1 ),
array( 11, 6, 6, 6, 5, 2 ),
array( 11, 6, 6, 6, 4, 3 ),
array( 11, 6, 6, 5, 5, 3 ),
array( 11, 6, 6, 5, 4, 4 ),
array( 11, 6, 5, 5, 5, 4 ),
array( 11, 5, 5, 5, 5, 5 ),
array( 10, 10, 10, 6, 0, 0 ),
array( 10, 10, 10, 5, 1, 0 ),
array( 10, 10, 10, 4, 2, 0 ),
array( 10, 10, 10, 4, 1, 1 ),
array( 10, 10, 10, 3, 3, 0 ),
array( 10, 10, 10, 3, 2, 1 ),
array( 10, 10, 10, 2, 2, 2 ),
array( 10, 10, 9, 7, 0, 0 ),
array( 10, 10, 9, 6, 1, 0 ),
array( 10, 10, 9, 5, 2, 0 ),
array( 10, 10, 9, 5, 1, 1 ),
array( 10, 10, 9, 4, 3, 0 ),
array( 10, 10, 9, 4, 2, 1 ),
array( 10, 10, 9, 3, 3, 1 ),
array( 10, 10, 9, 3, 2, 2 ),
array( 10, 10, 8, 8, 0, 0 ),
array( 10, 10, 8, 7, 1, 0 ),
array( 10, 10, 8, 6, 2, 0 ),
array( 10, 10, 8, 6, 1, 1 ),
array( 10, 10, 8, 5, 3, 0 ),
array( 10, 10, 8, 5, 2, 1 ),
array( 10, 10, 8, 4, 4, 0 ),
array( 10, 10, 8, 4, 3, 1 ),
array( 10, 10, 8, 4, 2, 2 ),
array( 10, 10, 8, 3, 3, 2 ),
array( 10, 10, 7, 7, 2, 0 ),
array( 10, 10, 7, 7, 1, 1 ),
array( 10, 10, 7, 6, 3, 0 ),
array( 10, 10, 7, 6, 2, 1 ),
array( 10, 10, 7, 5, 4, 0 ),
array( 10, 10, 7, 5, 3, 1 ),
array( 10, 10, 7, 5, 2, 2 ),
array( 10, 10, 7, 4, 4, 1 ),
array( 10, 10, 7, 4, 3, 2 ),
array( 10, 10, 7, 3, 3, 3 ),
array( 10, 10, 6, 6, 4, 0 ),
array( 10, 10, 6, 6, 3, 1 ),
array( 10, 10, 6, 6, 2, 2 ),
array( 10, 10, 6, 5, 5, 0 ),
array( 10, 10, 6, 5, 4, 1 ),
array( 10, 10, 6, 5, 3, 2 ),
array( 10, 10, 6, 4, 4, 2 ),
array( 10, 10, 6, 4, 3, 3 ),
array( 10, 10, 5, 5, 5, 1 ),
array( 10, 10, 5, 5, 4, 2 ),
array( 10, 10, 5, 5, 3, 3 ),
array( 10, 10, 5, 4, 4, 3 ),
array( 10, 10, 4, 4, 4, 4 ),
array( 10, 9, 9, 8, 0, 0 ),
array( 10, 9, 9, 7, 1, 0 ),
array( 10, 9, 9, 6, 2, 0 ),
array( 10, 9, 9, 6, 1, 1 ),
array( 10, 9, 9, 5, 3, 0 ),
array( 10, 9, 9, 5, 2, 1 ),
array( 10, 9, 9, 4, 4, 0 ),
array( 10, 9, 9, 4, 3, 1 ),
array( 10, 9, 9, 4, 2, 2 ),
array( 10, 9, 9, 3, 3, 2 ),
array( 10, 9, 8, 8, 1, 0 ),
array( 10, 9, 8, 7, 2, 0 ),
array( 10, 9, 8, 7, 1, 1 ),
array( 10, 9, 8, 6, 3, 0 ),
array( 10, 9, 8, 6, 2, 1 ),
array( 10, 9, 8, 5, 4, 0 ),
array( 10, 9, 8, 5, 3, 1 ),
array( 10, 9, 8, 5, 2, 2 ),
array( 10, 9, 8, 4, 4, 1 ),
array( 10, 9, 8, 4, 3, 2 ),
array( 10, 9, 8, 3, 3, 3 ),
array( 10, 9, 7, 7, 3, 0 ),
array( 10, 9, 7, 7, 2, 1 ),
array( 10, 9, 7, 6, 4, 0 ),
array( 10, 9, 7, 6, 3, 1 ),
array( 10, 9, 7, 6, 2, 2 ),
array( 10, 9, 7, 5, 5, 0 ),
array( 10, 9, 7, 5, 4, 1 ),
array( 10, 9, 7, 5, 3, 2 ),
array( 10, 9, 7, 4, 4, 2 ),
array( 10, 9, 7, 4, 3, 3 ),
array( 10, 9, 6, 6, 5, 0 ),
array( 10, 9, 6, 6, 4, 1 ),
array( 10, 9, 6, 6, 3, 2 ),
array( 10, 9, 6, 5, 5, 1 ),
array( 10, 9, 6, 5, 4, 2 ),
array( 10, 9, 6, 5, 3, 3 ),
array( 10, 9, 6, 4, 4, 3 ),
array( 10, 9, 5, 5, 5, 2 ),
array( 10, 9, 5, 5, 4, 3 ),
array( 10, 9, 5, 4, 4, 4 ),
array( 10, 8, 8, 8, 2, 0 ),
array( 10, 8, 8, 8, 1, 1 ),
array( 10, 8, 8, 7, 3, 0 ),
array( 10, 8, 8, 7, 2, 1 ),
array( 10, 8, 8, 6, 4, 0 ),
array( 10, 8, 8, 6, 3, 1 ),
array( 10, 8, 8, 6, 2, 2 ),
array( 10, 8, 8, 5, 5, 0 ),
array( 10, 8, 8, 5, 4, 1 ),
array( 10, 8, 8, 5, 3, 2 ),
array( 10, 8, 8, 4, 4, 2 ),
array( 10, 8, 8, 4, 3, 3 ),
array( 10, 8, 7, 7, 4, 0 ),
array( 10, 8, 7, 7, 3, 1 ),
array( 10, 8, 7, 7, 2, 2 ),
array( 10, 8, 7, 6, 5, 0 ),
array( 10, 8, 7, 6, 4, 1 ),
array( 10, 8, 7, 6, 3, 2 ),
array( 10, 8, 7, 5, 5, 1 ),
array( 10, 8, 7, 5, 4, 2 ),
array( 10, 8, 7, 5, 3, 3 ),
array( 10, 8, 7, 4, 4, 3 ),
array( 10, 8, 6, 6, 6, 0 ),
array( 10, 8, 6, 6, 5, 1 ),
array( 10, 8, 6, 6, 4, 2 ),
array( 10, 8, 6, 6, 3, 3 ),
array( 10, 8, 6, 5, 5, 2 ),
array( 10, 8, 6, 5, 4, 3 ),
array( 10, 8, 6, 4, 4, 4 ),
array( 10, 8, 5, 5, 5, 3 ),
array( 10, 8, 5, 5, 4, 4 ),
array( 10, 7, 7, 7, 5, 0 ),
array( 10, 7, 7, 7, 4, 1 ),
array( 10, 7, 7, 7, 3, 2 ),
array( 10, 7, 7, 6, 6, 0 ),
array( 10, 7, 7, 6, 5, 1 ),
array( 10, 7, 7, 6, 4, 2 ),
array( 10, 7, 7, 6, 3, 3 ),
array( 10, 7, 7, 5, 5, 2 ),
array( 10, 7, 7, 5, 4, 3 ),
array( 10, 7, 7, 4, 4, 4 ),
array( 10, 7, 6, 6, 6, 1 ),
array( 10, 7, 6, 6, 5, 2 ),
array( 10, 7, 6, 6, 4, 3 ),
array( 10, 7, 6, 5, 5, 3 ),
array( 10, 7, 6, 5, 4, 4 ),
array( 10, 7, 5, 5, 5, 4 ),
array( 10, 6, 6, 6, 6, 2 ),
array( 10, 6, 6, 6, 5, 3 ),
array( 10, 6, 6, 6, 4, 4 ),
array( 10, 6, 6, 5, 5, 4 ),
array( 10, 6, 5, 5, 5, 5 ),
array( 9, 9, 9, 9, 0, 0 ),
array( 9, 9, 9, 8, 1, 0 ),
array( 9, 9, 9, 7, 2, 0 ),
array( 9, 9, 9, 7, 1, 1 ),
array( 9, 9, 9, 6, 3, 0 ),
array( 9, 9, 9, 6, 2, 1 ),
array( 9, 9, 9, 5, 4, 0 ),
array( 9, 9, 9, 5, 3, 1 ),
array( 9, 9, 9, 5, 2, 2 ),
array( 9, 9, 9, 4, 4, 1 ),
array( 9, 9, 9, 4, 3, 2 ),
array( 9, 9, 9, 3, 3, 3 ),
array( 9, 9, 8, 8, 2, 0 ),
array( 9, 9, 8, 8, 1, 1 ),
array( 9, 9, 8, 7, 3, 0 ),
array( 9, 9, 8, 7, 2, 1 ),
array( 9, 9, 8, 6, 4, 0 ),
array( 9, 9, 8, 6, 3, 1 ),
array( 9, 9, 8, 6, 2, 2 ),
array( 9, 9, 8, 5, 5, 0 ),
array( 9, 9, 8, 5, 4, 1 ),
array( 9, 9, 8, 5, 3, 2 ),
array( 9, 9, 8, 4, 4, 2 ),
array( 9, 9, 8, 4, 3, 3 ),
array( 9, 9, 7, 7, 4, 0 ),
array( 9, 9, 7, 7, 3, 1 ),
array( 9, 9, 7, 7, 2, 2 ),
array( 9, 9, 7, 6, 5, 0 ),
array( 9, 9, 7, 6, 4, 1 ),
array( 9, 9, 7, 6, 3, 2 ),
array( 9, 9, 7, 5, 5, 1 ),
array( 9, 9, 7, 5, 4, 2 ),
array( 9, 9, 7, 5, 3, 3 ),
array( 9, 9, 7, 4, 4, 3 ),
array( 9, 9, 6, 6, 6, 0 ),
array( 9, 9, 6, 6, 5, 1 ),
array( 9, 9, 6, 6, 4, 2 ),
array( 9, 9, 6, 6, 3, 3 ),
array( 9, 9, 6, 5, 5, 2 ),
array( 9, 9, 6, 5, 4, 3 ),
array( 9, 9, 6, 4, 4, 4 ),
array( 9, 9, 5, 5, 5, 3 ),
array( 9, 9, 5, 5, 4, 4 ),
array( 9, 8, 8, 8, 3, 0 ),
array( 9, 8, 8, 8, 2, 1 ),
array( 9, 8, 8, 7, 4, 0 ),
array( 9, 8, 8, 7, 3, 1 ),
array( 9, 8, 8, 7, 2, 2 ),
array( 9, 8, 8, 6, 5, 0 ),
array( 9, 8, 8, 6, 4, 1 ),
array( 9, 8, 8, 6, 3, 2 ),
array( 9, 8, 8, 5, 5, 1 ),
array( 9, 8, 8, 5, 4, 2 ),
array( 9, 8, 8, 5, 3, 3 ),
array( 9, 8, 8, 4, 4, 3 ),
array( 9, 8, 7, 7, 5, 0 ),
array( 9, 8, 7, 7, 4, 1 ),
array( 9, 8, 7, 7, 3, 2 ),
array( 9, 8, 7, 6, 6, 0 ),
array( 9, 8, 7, 6, 5, 1 ),
array( 9, 8, 7, 6, 4, 2 ),
array( 9, 8, 7, 6, 3, 3 ),
array( 9, 8, 7, 5, 5, 2 ),
array( 9, 8, 7, 5, 4, 3 ),
array( 9, 8, 7, 4, 4, 4 ),
array( 9, 8, 6, 6, 6, 1 ),
array( 9, 8, 6, 6, 5, 2 ),
array( 9, 8, 6, 6, 4, 3 ),
array( 9, 8, 6, 5, 5, 3 ),
array( 9, 8, 6, 5, 4, 4 ),
array( 9, 8, 5, 5, 5, 4 ),
array( 9, 7, 7, 7, 6, 0 ),
array( 9, 7, 7, 7, 5, 1 ),
array( 9, 7, 7, 7, 4, 2 ),
array( 9, 7, 7, 7, 3, 3 ),
array( 9, 7, 7, 6, 6, 1 ),
array( 9, 7, 7, 6, 5, 2 ),
array( 9, 7, 7, 6, 4, 3 ),
array( 9, 7, 7, 5, 5, 3 ),
array( 9, 7, 7, 5, 4, 4 ),
array( 9, 7, 6, 6, 6, 2 ),
array( 9, 7, 6, 6, 5, 3 ),
array( 9, 7, 6, 6, 4, 4 ),
array( 9, 7, 6, 5, 5, 4 ),
array( 9, 7, 5, 5, 5, 5 ),
array( 9, 6, 6, 6, 6, 3 ),
array( 9, 6, 6, 6, 5, 4 ),
array( 9, 6, 6, 5, 5, 5 ),
array( 8, 8, 8, 8, 4, 0 ),
array( 8, 8, 8, 8, 3, 1 ),
array( 8, 8, 8, 8, 2, 2 ),
array( 8, 8, 8, 7, 5, 0 ),
array( 8, 8, 8, 7, 4, 1 ),
array( 8, 8, 8, 7, 3, 2 ),
array( 8, 8, 8, 6, 6, 0 ),
array( 8, 8, 8, 6, 5, 1 ),
array( 8, 8, 8, 6, 4, 2 ),
array( 8, 8, 8, 6, 3, 3 ),
array( 8, 8, 8, 5, 5, 2 ),
array( 8, 8, 8, 5, 4, 3 ),
array( 8, 8, 8, 4, 4, 4 ),
array( 8, 8, 7, 7, 6, 0 ),
array( 8, 8, 7, 7, 5, 1 ),
array( 8, 8, 7, 7, 4, 2 ),
array( 8, 8, 7, 7, 3, 3 ),
array( 8, 8, 7, 6, 6, 1 ),
array( 8, 8, 7, 6, 5, 2 ),
array( 8, 8, 7, 6, 4, 3 ),
array( 8, 8, 7, 5, 5, 3 ),
array( 8, 8, 7, 5, 4, 4 ),
array( 8, 8, 6, 6, 6, 2 ),
array( 8, 8, 6, 6, 5, 3 ),
array( 8, 8, 6, 6, 4, 4 ),
array( 8, 8, 6, 5, 5, 4 ),
array( 8, 8, 5, 5, 5, 5 ),
array( 8, 7, 7, 7, 7, 0 ),
array( 8, 7, 7, 7, 6, 1 ),
array( 8, 7, 7, 7, 5, 2 ),
array( 8, 7, 7, 7, 4, 3 ),
array( 8, 7, 7, 6, 6, 2 ),
array( 8, 7, 7, 6, 5, 3 ),
array( 8, 7, 7, 6, 4, 4 ),
array( 8, 7, 7, 5, 5, 4 ),
array( 8, 7, 6, 6, 6, 3 ),
array( 8, 7, 6, 6, 5, 4 ),
array( 8, 7, 6, 5, 5, 5 ),
array( 8, 6, 6, 6, 6, 4 ),
array( 8, 6, 6, 6, 5, 5 ),
array( 7, 7, 7, 7, 7, 1 ),
array( 7, 7, 7, 7, 6, 2 ),
array( 7, 7, 7, 7, 5, 3 ),
array( 7, 7, 7, 7, 4, 4 ),
array( 7, 7, 7, 6, 6, 3 ),
array( 7, 7, 7, 6, 5, 4 ),
array( 7, 7, 7, 5, 5, 5 ),
array( 7, 7, 6, 6, 6, 4 ),
array( 7, 7, 6, 6, 5, 5 ),
array( 7, 6, 6, 6, 6, 5 ),
array( 6, 6, 6, 6, 6, 6 ),
);