Problem:
Score : 400 points

Problem Statement

A positive integer X is said to be a lunlun number if and only if the following condition is satisfied:

In the base ten representation of X (without leading zeros), for every pair of two adjacent digits, the absolute difference of those digits is at most 1.

For example, 1234, 1, and 334 are lunlun numbers, while none of 31415, 119, or 13579 is.

You are given a positive integer K. Find the K-th smallest lunlun number.

Constraints

1 \leq K \leq 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

K

Output

Print the answer.

Sample Input 1

15

Sample Output 1

23

We will list the 15 smallest lunlun numbers in ascending order:

1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
21,
22,
23.

Thus, the answer is 23.

Sample Input 2

1

Sample Output 2

1

Sample Input 3

13

Sample Output 3

21

Sample Input 4

100000

Sample Output 4

3234566667

Note that the answer may not fit into the 32-bit signed integer type.

Solution in LuaJIT (2.0.4) (judge verdict: Accepted)

---- Quote(Alteration) ----
Queue = {}

function Queue.new()
    local obj = { buff = {}, top_index = 0}
    return setmetatable(obj,{__index = Queue})
end

function Queue:enqueue(x)
    table.insert(self.buff, x)
end

function Queue:dequeue()
    self.top_index = self.top_index + 1
    local value = self.buff[self.top_index]
    self.buff[self.top_index] = nil
    return value
end
--[[
function Queue:top()
    if #self.buff > 0 then
        return self.buff[self.top_index]
    end
end
--
function Queue:isEmpty()
    return #self.buff == 0
end
--]]
---- from http://www.nct9.ne.jp/m_hiroi/light/lua.html ----


--[[
ルンルン数の特徴:十以上の位がそれまでに出て来たルンルン数を流用している。
それゆえ、流用される側の数字の一の位に-1, 0, 1を加えた数と
流用される側の数字を10倍した数を足し、ルンルン数を生成する。
ただし、流用される側の数字の一の位の数字が0,9のときは生成しない場合を作っておく。
]]
local k = io.read("*n")
local lunluns = Queue.new()
for i = 1, 9 do
    lunluns:enqueue(i)
    if i == k then
        print(tostring(i)); os.exit()
    end
end

for i = 1, k do
    local x = 0LL + lunluns:dequeue()
    if x % 10 ~= 0 then
        lunluns:enqueue(10 * x + (x % 10) - 1)
        if #lunluns.buff == k then
            print(tostring(10 * x + (x % 10) - 1):sub(1, -3)); break
        end
    end
    lunluns:enqueue(10 * x + (x % 10))
    if #lunluns.buff == k then
        print(tostring(10 * x + (x % 10)):sub(1, -3)); break
    end
    if x % 10 ~= 9 then
        lunluns:enqueue(10 * x + (x % 10) + 1)
        if #lunluns.buff == k then
            print(tostring(10 * x + (x % 10) + 1):sub(1, -3)); break
        end
    end
end