The Haar basis, proof of orthonormality.

Question

Please i have this problem and i known how to prove completeness but do not know how to prove that it is orthonormal. I will appreciate it if anyone can help me. Given that $n\geq1$ write $n=k+2^p$,where $p\geq0$ and $k\geq0$ are integers uniquely determined by the condition $k\leq2^p-1$. consider the function defined on $(0,1)$ by$$\psi_{n}(t)=\begin{cases} 2^{p/2}, & 2^{-p}k < t < 2^{-p}(k+1/2)\\-2^{p/2} ,& 2^{-p}(k+1/2) < t < 2^{-p}(k+1) \\ 0, & \textrm{otherwise.} \end{cases}$$ Set $\psi_0\equiv$ 1 and prove that $(\psi_n)_{n\geq0}$ is an orthonormal basis of $L^2(0,1)$.