A long air-cored solenoid has $N$ turns, length $l$ and area $A$. Six statements about changes follow. (i) Doubling $N$ makes the self-inductance $L$ four times as large. (ii) Doubling the radius makes $L$ twice as large. (iii) Doubling the length, with $N$ and $A$ fixed, halves $L$. (iv) Doubling the current doubles the stored energy. (v) A short iron core in its middle multiplies $L$ by $\mu_r$. (vi) $L$ depends on the current in an air-cored solenoid. How many of the statements above are correct?