Given a finite dimensional algebra $A$ with two indecomposable modules $M$ and $N$. Define $H(M,N)$ as the largest number of indecomposable summands of a module $X$ such that there exists a non-split short exact sequence $0 \rightarrow N \rightarrow X \rightarrow M \rightarrow 0$. Let $R_i$ be a basis of $Ext_A^1(M,N)$ such that $R_i$ is representated by short exact sequences with middle terms $X_i$. Let $|W|$ denote the number of indecomposable summands of a module $W$.
Question: Is it true that $H(M,N)$ is equal to the largest number of the $|X_i|$ independent of the choice of a basis?