local fmt = require "fmt"
require "table2"

local function ndigits(x)
    local n = 0
    while x > 0 do
        n += 1
        x //= 10
    end
    return n
end

local function dtally(x)
    local t = 0
    while x > 0 do
        t += 2 ** ((x % 10) * 6)
        x //= 10
    end
    return t
end

local tens = table.rep(15, 0)

local function init()
    tens[1] = 1
    for i = 2, 15 do tens[i] = tens[i - 1] * 10 end
end

local function fangs(x)
    local f = {}
    local nd = ndigits(x)
    if nd & 1 == 1 then return f end
    nd //= 2
    local lo = math.max(tens[nd], (x + tens[nd + 1] - 2) // (tens[nd + 1] - 1))
    local hi = math.min(x // lo, math.floor(math.sqrt(x)))
    local t = dtally(x)
    local a = lo
    while a <= hi do
        local b = x // a
        local t2 = dtally(a) + dtally(b)
        if a * b == x and ((a % 10) > 0 or (b % 10) > 0) and t == t2 then
            f:insert(a)
        end
        a += 1
    end
    return f
end

local function showfangs(x, f)
    fmt.write("%6d", x)
    if #f > 1 then print() end
    for f as a do fmt.print(" = %3d x %3d", a, x // a) end
end

init()
local x = 1
local n = 0
while n < 25 do
    local f = fangs(x)
    if #f > 0 then
        n += 1
        fmt.write("%2d: ", n)
        showfangs(x, f)
    end
    x += 1
end
print()
for {16758243290880, 24959017348650, 14593825548650} as y do
    local f = fangs(y)
    if #f > 0 then
        showfangs(y, f)
    else
        fmt.print("%d is not vampiric", y)
    end
end