Multiplications in fast exponentiation

You compute $a^{45}$ by left-to-right binary (square-and-multiply) exponentiation, run exactly as follows: read the exponent's bits from the most significant down; initialize the running result to $a$, which consumes the leading $1$-bit for free (no multiply); then for each remaining lower bit, square the running result, and — only where that bit is $1$ — also multiply by $a$. Counting every squaring and every multiply-by-$a$, exactly how many multiplications does the whole computation take?