Young tablaux and its shape: a basic question

Question

Let $D$ and $D'$ be Young tablaux w.r.t. partitions $(n_1\ge \cdots n_r)$ and $(m_1\ge \cdots \ge m_s)$ of $n$. Suppose that

• If $\alpha,\beta$ are in same row of $D$ then $\alpha,\beta$ lie in different columns of $D'$.
• If $\alpha',\beta'$ are in same row of $D'$ then $\alpha',\beta'$ lie in different columns of $D$.

Question. Can we conclude that $D$ and $D'$ have same shape (i.e. $n_1=m_1$, $n_2=m_2$, $\cdots$)?