Pure silicon at room temperature has $1.5 \times 10^{16}$ free electrons per cubic metre, and the same number of holes. It is doped with $4.5 \times 10^{22}$ donor (pentavalent) atoms per cubic metre, each of which gives one free electron. If the number of holes per cubic metre in the doped silicon is $N \times 10^{9}$, the value of N is ____.