  For any channel $P_{Y|X}$ the strong data processing constant is defined as
the smallest number $\eta_{KL}\in[0,1]$ such that $I(U;Y)\le \eta_{KL} I(U;X)$
holds for any Markov chain $U-X-Y$. It is shown that the value of $\eta_{KL}$
is given by that of the best binary-input subchannel of $P_{Y|X}$. The same
result holds for any $f$-divergence, verifying a conjecture of Cohen, Kemperman
and Zbaganu (1998).
