You are given coins of different denominations and a total amount of money amount. Write a function to compute the fewest number of coins that you need to make up that amount. If that amount of money cannot be made up by any combination of the coins, return -1.
You may assume that you have an infinite number of each kind of coin.
 
Example 1:
Input: coins = [1,2,5], amount = 11
Output: 3
Explanation: 11 = 5 + 5 + 1

Example 2:
Input: coins = [2], amount = 3
Output: -1

Example 3:
Input: coins = [1], amount = 0
Output: 0

Example 4:
Input: coins = [1], amount = 1
Output: 1

Example 5:
Input: coins = [1], amount = 2
Output: 2

 
Constraints:

1 <= coins.length <= 12
1 <= coins[i] <= 231 - 1
0 <= amount <= 104

```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 = 'class Solution:\n    def coinChange(self, coins: List[int], amount: int) -> int:\n        \'\'\'\n        dp = [float(\'inf\')]*(amount+1)\n        dp[0] = 0\n        \n        for coin in coins:\n            for x in range(coin, amount+1):\n                if coin <= x:\n                    dp[x] = min(dp[x], dp[x-coin]+1)\n                \n        return dp[amount] if dp[amount] != float(\'inf\') else -1\n        \'\'\'\n        \'\'\'\n        def helper(amount):\n            if amount < 0:\n                return -1\n            elif amount == 0:\n                return 0\n            minCoins = None\n            for coin in coins:\n                totCoins = 1 + helper(amount - coin)\n                \n                if totCoins > 0 and (minCoins is None or totCoins < minCoins):\n                    minCoins = totCoins\n            if minCoins is None:\n                return -1\n            else:\n                return minCoins\n        return helper(amount)\n        \'\'\'\n        def dfs(start, amt, n_coins):\n            nonlocal min_coins\n\n            coin = coins[start]\n\n            # LHS = lower bound on number of coins, achieved using the current coin\n            # Return early since we can\'t possibly achieve original \\"amount\\"\n            # along this path.\n            # For this particular solution, this check isn\'t necessarily,\n            # since there is another check within the loop below. However, it\n            # speeds up the solution. Better to have this check before the\n            # \\"amt == 0\\" check below.\n            #if n_coins + (amt + coin - 1) / coin > min_coins:\n            #if (min_coins - n_coins - 1) * coin + 1 < amt:\n            #    return\n\n            div = amt // coin\n            n_coins += div\n            amt %= coin\n            \n            if amt == 0:\n                min_coins = min(min_coins, n_coins)\n                return\n            \n            if start < len_coins:\n                # use as many of current coin as possible, and try next smaller coin\n                dfs(start + 1, amt, n_coins)\n\n                # Always greedily taking as many of biggest coins as possible doesn\'t work.\n                # \\"Backtrack\\" by using 1 less of current coin per iteration, and\n                # trying the next smaller coin.\n\n                next_coin = coins[start + 1]\n                \n                for _ in range(div):\n                    amt += coin \n                    n_coins -= 1\n                    \n                    if (min_coins - n_coins - 1) * next_coin + 1 > amt:\n                    #if (min_coins - n_coins) * next_coin > amt: # hope still exists\n                        dfs(start + 1, amt, n_coins)\n                    else:\n                        break\n        \n        len_coins = len(coins) - 1\n        \n        # try biggest coins first\n        coins.sort(reverse=True)\n        \n        min_coins = float(\'inf\')\n\n        dfs(0, amount, 0)\n        \n        return min_coins if min_coins < float(\'inf\') else -1'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'coinChange'
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: 6492