Infinite matrix of non negative numbers (sequence)

Question

Suppose that we have matrix $\begin{Bmatrix}a_{ij}\end{Bmatrix}_{n = 1}^{\infty}$ of non negative real numbers. Let $\pi : \mathbb{N}\rightarrow \mathbb{N} \times \mathbb{N}$ be bijection so $\begin{Bmatrix}a_{\pi _{1}(n)\pi _{2}(n)}\end{Bmatrix}_{n = 1}^{\infty}$ is a rearrangement of the matrix. Prove that $$\sum_{n = 1}^{\infty}a_{ \pi _{1}(n)\pi _{2}(n)}$$ and $$\sum_{j = 1}^{\infty}(\sum_{i = 1}^{\infty} a_{ij})$$ are both convergent (and their sums are equal) or both divergent. Any ideas? Thanks in advance!