function string.remove(s, str)
    s = tostring(s)
    local a, b = s:match("(.-)" .. str .. "(.+)")
    return (a and b) and a .. b or s, s:find(str) and #s-s:find(str) or 0
end

function sum(a, b)
    local ret = ""
    a, na = string.remove(a, "%-")
    b, nb = string.remove(b, "%-")
    a = ("0"):rep(#b-#a) .. a
    b = ("0"):rep(#a-#b) .. b
    if (na == 0 and nb == 0) or (na ~= 0 and nb ~= 0) then
        local reminder = 0
        for i = #a, 1, -1 do
            local v = tonumber(a:sub(i, i))+tonumber(b:sub(i, i))+reminder
            if v < 10 then
                reminder = 0
                ret = v .. ret
            else
                reminder = tonumber(tostring(v):sub(1, 1))
                ret = tostring(v):sub(#tostring(v)) .. ret
            end
        end
        if reminder ~= 0 then
            ret = reminder .. ret
        end
    end
    if na ~= 0 and nb ~= 0 then
        ret = "-" .. ret
    end
    return ret
end

function dif(a, b)
    local ret = ""
    a, na = string.remove(a, "%-")
    b, nb = string.remove(b, "%-")
    a = ("0"):rep(#b-#a) .. a
    b = ("0"):rep(#a-#b) .. b
    if bigger(b, a) then
        local ba = a
        a = b
        b = ba
    end
    local reminder = 0
    for i = #a, 1, -1 do
        local v = tonumber(a:sub(i, i))-tonumber(b:sub(i, i))-reminder
        if v < 0 then
            v = v+10
            reminder = 1
            ret = v .. ret
        else
            reminder = 0
            ret = v .. ret
        end
    end
    return ret
end

function prod(a, b)
    local ret = ""
    local values = {}
    local reminder = 0
    a, ca = string.remove(a, "%.")
    b, cb = string.remove(b, "%.")
    a, na = string.remove(a, "%-")
    b, nb = string.remove(b, "%-")
    for ia = #a, 1, -1 do
        for ib = #b, 1, -1 do
            local v = tonumber(a:sub(ia, ia))*tonumber(b:sub(ib, ib))+reminder
            if v < 10 then
                reminder = 0
                ret = v .. ret
            else
                reminder = tonumber(tostring(v):sub(1, 1))
                ret = tostring(v):sub(#tostring(v)) .. ret
            end
        end
        if reminder ~= 0 then
            ret = reminder .. ret
        end
        table.insert(values, ret)
        ret = ""
        reminder = 0
    end
    local total = "0"
    for i = 1, #values do
        total = sum(total, values[i] .. ("0"):rep(i-1))
    end
    if ca+cb > 0 then
        total = total:sub(1, #total-ca-cb) .. "." .. total:sub(#total-ca-cb+1)
    end
    if (na ~= 0 and nb == 0) or (nb ~= 0 and na == 0) then
        total = "-" .. total
    end
    return total
end

function bigger(a, b)
    a = ("0"):rep(#b-#a) .. a
    b = ("0"):rep(#a-#b) .. b
    for i = 1, #a do
        if tonumber(a:sub(i, i)) > tonumber(b:sub(i, i)) then
            return true
        elseif tonumber(a:sub(i, i)) < tonumber(b:sub(i, i)) then
            return false
        end
    end
end

function table.reverse(tab)
    local ret = {}
    for i = #tab, 1, -1 do
        table.insert(ret, tab[i])
    end
    return ret
end

function mathfloor(str)
    return str:match("(.+)%.") or str
end

function sqroot(n, amount)
    amount = amount+1
    local npairs = {}
    local root = ""
    n = tostring(n)
    for i = 1, #n, 2 do
        table.insert(npairs, n:sub(#n-i, #n-i+1))
    end
    npairs = table.reverse(npairs)
    root = root .. mathfloor(tostring(math.sqrt(tonumber(npairs[1]))))
    local rest = tostring(tonumber(npairs[1])-math.floor(math.sqrt(tonumber(npairs[1])))^2)
    local nextvalue = 2
    local comma
    while rest and bigger(rest, "0") and #root < amount  do
        if npairs[nextvalue] then
            rest = rest .. npairs[nextvalue]
        else
            rest = rest .. "00"
            if not comma then
                comma = nextvalue
            end
        end
        droot = prod(root, 2) .. "0"
        while bigger(rest, prod(droot, droot:sub(#droot))) and bigger("9", droot:sub(#droot)) do
            droot = droot:sub(1, #droot-1) .. sum(droot:sub(#droot), "1")
        end
        if bigger(prod(droot, droot:sub(#droot)), rest) then
            droot = droot:sub(1, #droot-1) .. dif(droot:sub(#droot), "1")
        end
        root = root .. droot:sub(#droot)
        rest = dif(rest, prod(droot, droot:sub(#droot)))
        nextvalue = nextvalue+1
    end
    if comma then
        return root:sub(1, comma-1) .. "." .. root:sub(comma)
    else
        return root
    end
end