our $C;
for my $k (0 .. $N - 1) {
	for my $l (0 .. $N - 1) {
		my $e;
		if (0 == $k) {
			if (0 == $l) {
				$e = 1;
			} else {
				$e = 0;
			}
		} else {
			$e = 0;
			if (0 < $l) {
				$e += $$C[$k-1][$l-1];
			}
			if ($l < $N - 1) {
				$e += $$C[$k-1][$l+1];
			}
		}
		$$C[$k][$l] = $e;
	}
}

our $U;
for my $k (0 .. $N - 1) {
	for my $l (0 .. $N - 1) {
		my $e;
		if (0 == $k) {
			if (0 == $l) {
				$e = 1;
			} else {
				$e = 0;
			}
		} elsif (1 == $k) {
			if (1 == $l) {
				$e = 2;
			} else {
				$e = 0;
			}
		} else {
			$e = -$$U[$k-2][$l];
			if (0 < $l) {
				$e += 2 * $$U[$k-1][$l-1];
			}
		}
		$$U[$k][$l] = $e;
	}
}