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        self.memo = {0: 0}\n        \n        coins.sort()\n    \n        self.getMinCoins(coins, amount)\n        \n        if self.memo[amount] == float('inf'):\n            \n            return(-1)\n        \n        return(self.memo[amount])\n    \n    def getMinCoins(self, coins, amount):\n        \n        \n        if amount in self.memo:\n            \n            return(self.memo[amount])\n        \n        minCoins = float('inf')\n        \n        for coin in coins:\n            \n            if amount - coin < 0:\n                \n                break\n                \n            currCoins = self.getMinCoins(coins, amount - coin) + 1\n            minCoins = min(minCoins, currCoins)\n            \n        self.memo[amount] = minCoins\n        \n        return(self.memo[amount])\n        \n        \n#         numCoins = len(coins)\n        \n#         # Values in this array equal the number of coins needed to achieve the cost of the index\n#         minCoins = [amount + 1] * (amount + 1)\n#         minCoins[0] = 0\n        \n#         # Loop through every needed amount\n#         for i in range(amount + 1):\n#             # Loop through every coin value\n#             for coin in coins:\n#                 # Check that the coin is not bigger than the current amount\n#                 if coin <= i:\n#                     # minCoins[i]: number of coins needed to make amount i\n#                     # minCoins[i-coin]: number of coins needed to make the amount before adding \n#                     #                   the current coin to it (+1 to add the current coin)\n#                     minCoins[i] = min(minCoins[i], minCoins[i-coin] + 1)\n        \n#         # Check if any combination of coins was found to create the amount\n#         if minCoins[amount] == amount + 1:\n#             return -1\n        \n#         # Return the optimal number of coins to create the amount\n#         return minCoins[amount]\n"
_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: 8856