# 多項係数 Multinomial Coefficient
# 引数 数値 (\@N)
# 戻り値 多項係数 ($MultinomialCoefficient)
sub MULTINOMIALCOEFFICIENT{
	my ($N) = @_;
	my $MultinomialCoefficient = 1;
	my @NaturalNumber = ();
	my $Factorial = 1;
	my $Highest = 1;
	my $SumN = 0;
	my $Count = @N - 1;
	
	# 値の確認
	for(my $i = 0; $i <= $Count; $i++){
		if($N[$i] < 0){
			return 0;
		}else {
			$NaturalNumber[$i] = int($N[$i]);
			$SumN += $NaturalNumber[$i];
		}
	
		# 最も高い数値を階乗の計算から除外
		if($NaturalNumber[$i] > $Highest){
			$Highest = $NaturalNumber[$i];
		}	
	}
	
	# 階乗
	for(my $i = $SumN; $i > $Highest; $i--){
		$Factorial = $Factorial * $i;
	}
	
	# 計算
	for(my $i = $Count; $i >= 0; $i--){
		if($NaturalNumber[$i] != $Highest){
			for(my $j = $NaturalNumber[$i]; $j >= 2; $j--){
				$Factorial = $Factorial / $j;		
			}
		}else {
			$Highest = 0;
		}
	}
	
	# 多項係数 Multinomial Coefficient
	$MultinomialCoefficient = $Factorial;
	
	return $MultinomialCoefficient;
}