Try this one, and let me know if it is not working.

by

by

by

by

and then define

by

by

by

Then, .

This seems like a snake lemma. To apply a snake lemma, the necessary conditions arethe kernel would be (I guess?)

because the rows are exact.

f_1 is a monomorphism and g_2 is an epimorphism.

So I think we can apply a snake lemma here.