Publicly verifiable secret sharing scheme

In https://www.win.tue.nl/~berry/papers/crypto99.pdf, Schoenmakers proposes a publicly verifiable secret sharing scheme, that uses a non-interactive DLEQ proof to allow any participant to verify the shares of the secret (section 3.1 of the paper).

In “Distribution of the shares”, it says “Applying Fiat-Shamir’s technique, the challenge $c$ for the protocol is computed as a cryptographic hash of $X_i , Y_i , a_{1i} , a_{2i} , 1 ≤ i ≤ n$.”

And later, “Using $y_i , X_i , Y_i , r_i , 1 ≤ i ≤ n$ and $c$ as input, the verifier computes $a_{1i} , a_{2i}$ as

$$a_{1i} = g^{ri} X_i^c,$$ $$a_{2i} = y_i^{ri} Y_i^c ,$$

and checks that the hash of $X_i , Y_i , a_{1i} , a_{2i} , 1 ≤ i ≤ n$, matches $c$.”

My question is: how can the challenge $c$ be used as input of the hash that computes itself (the challenge $c$), or am I misunderstanding?