require "table2"
require "perm"

local limit = 1_000_000

local function self_ref_seq(s)
    local sb = ""
    for "9876543210":split("") as d do
        if d in s then
            local count = s:split(""):count(|c| -> c == d)
            sb ..= $"{count}{d}"
        end
    end
    return sb
end

local sieve = table.rep(limit, 0)
local elements = {}
for n = 1, limit - 1 do
    if sieve[n + 1] == 0 then
        elements:clear()
        local next = tostring(n)
        elements:insert(next)
        while true do
            next = self_ref_seq(next)
            if next in elements then
                local size = #elements
                sieve[n + 1] = size
                if n > 9 then
                    local perms = perm.list(tostring(n):split("")):map(|p| -> p:concat(""))
                    perms = perms:dedup():reorder()
                    for perms as perm do
                        if perm[1] != "0" then
                            local k = tonumber(perm)
                            sieve[k + 1] = size
                        end
                    end
                end
                break
            end
            elements:insert(next)
        end
    end
end
local max_iterations = sieve:max()
for n = 1, limit - 1 do
    if sieve[n + 1] >= max_iterations then
        print($"{n} -> Iterations = {max_iterations}")
        local next = tostring(n)
        for i = 1, max_iterations do
            print(next)
            next = self_ref_seq(next)
        end
        print()
    end
end