Let $N$ be a positive integer. Prove that for any real numbers $\{w_{j, k}\}_{1 \leq j, k \leq N}$, $\{x_{k, l}\}_{1 \leq k, l \leq N}$, $\{y_{l, j}\}_{1 \leq l, j \leq N}$ one has \begin{align*} \sum_{1 \leq j, k, l \leq N}|w_{j, k}x_{k, l}y_{l, j}| \leq \left(\sum_{1 \leq j, k \leq N}|w_{j, k}|^2\right)^{\frac{1}{2}} \left(\sum_{1 \leq k, l \leq N}|x_{k, l}|^2\right)^{\frac{1}{2}} \left(\sum_{1 \leq l, j \leq N}|y_{l, j}|^2\right)^{\frac{1}{2}} \end{align*}
Being that we have been talking about the Cauchy-Schwarz inequality recently in class, and due to it's apparent similarity I think I am supposed to prove this in a similar manner to or with the Cauchy-Schwarz inequality. I'm am truly just stuck on where to start other than possibly squaring everything to move towards more similarity to the CS inequality: \begin{align*} \left|\sum_{1 \leq j, k, l \leq N}w_{j, k}x_{k, l}y_{l, j}\right|^2\leq \sum_{1 \leq j, k \leq N}|w_{j, k}|^2 \sum_{1 \leq k, l \leq N}|x_{k, l}|^2 \sum_{1 \leq l, j \leq N}|y_{l, j}|^2 \end{align*}
Also if someone could help explain what the two subscripts ($k, l$ in $x_{k,l}$) represent in relation to the real numbers I would appreciate it.
Thank you for any help.