Online calculator for fast-growing hierarchy with Buchholz function

Write a function of fast-growing hierarchy f_α(n) where "n" is a natural number and "α" is a countable ordinal, written in the normal form of Bichholz's function, i.e. α=0 or α=ψ₀(β₁)+...+ψ₀(β_k), where k≥1 and ψ₀(β₁)≥...≥ψ₀(β_k) and β_i∈C_νi(β_i) for 1≤i≤k. Each β_i should be written in the normal form too, i.e. β_i=0 or β_i=ψ_ν1(γ₁)+...+ψ_νm(γ_m). Also, due to limits of the programm, ν₁,..., ν_m should be digits from 0 to 9. Write "p" instead "ψ". For example, instead f_{ψ0(ψ1(0)+ψ1(0))}(100) write f_{p_0(p_1(0)+p_1(0))}(100). Don't use spaces.

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