# Task
 Given an integer `product`, find the smallest positive integer the product of whose digits is equal to product. If there is no such integer, return -1 instead.

# Example

 For `product = 1`, the output should be `11`;
 
 `1 x 1 = 1` (1 is not a valid result, because it has only 1 digit)
 
 For `product = 12`, the output should be `26`;
 
 `2 x 6 = 12`
 
 For `product = 19`, the output should be `-1`.
 
 No valid result found.
 
 For `product = 450`, the output should be `2559`.
 
 `2 x 5 x 5 x 9 = 450`
 
 For `product = 581`, the output should be `-1`.
 
 No valid result found. 
 
 Someone says the output should be `783`, because `7 x 83 = 581`.
 
 Please note: `83` is not a **DIGIT**.
 
# Input/Output


 - `[input]` integer `product`

    Constraints: `0 ≤ product ≤ 600`.


 - `[output]` a positive integer

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def digits_product(product):\n    if product<10:\n        return 10+product\n    res=factorization(product)\n    for i in res:\n        if i>=10:\n            return -1\n    reduce(res)\n    total=0\n    for i,j in enumerate(res):\n        total+=10**(len(res)-i-1)*j\n    return total\ndef factorization(n):\n    res=[]\n    factor=2\n    while factor*factor<=n:\n        if n%factor==0:\n            res.append(factor)\n            n//=factor\n            factor=2\n        else:\n            factor+=1\n    res.append(n)\n    return res\ndef is_prime(n):\n    for i in range(2, int(n**0.5)+1):\n        if n%i==0:\n            return False\n    return True\ndef reduce(res):\n    while res.count(3)>=2:\n        res.remove(3)\n        res.remove(3)\n        res.append(9)\n    while res.count(2)>=3:\n        res.remove(2)\n        res.remove(2)\n        res.remove(2)\n        res.append(8)\n    while res.count(2)>=1 and res.count(3)>=1:\n        res.remove(2)\n        res.remove(3)\n        res.append(6)\n    while res.count(2)>=2:\n        res.remove(2)\n        res.remove(2)\n        res.append(4)\n    res.sort()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'digits_product'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 6752