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        if amount < 1:\n            return 0\n        self.cache=[0] * (amount + 1)\n        return self.coin_change(coins, amount)\n\n    def coin_change(self, coins, remainder):\n        if remainder < 0:\n            return -1\n\n        if remainder == 0:\n            return 0\n\n        if self.cache[remainder] != 0:\n            return self.cache[remainder]\n\n        system_max = sys.maxsize\n        minimum = system_max\n        for coin in coins:\n            change_result = self.coin_change(coins, remainder - coin)\n\n            if (change_result >= 0 and change_result < minimum):\n                minimum = 1 + change_result\n\n        self.cache[remainder] = -1 if (minimum == system_max) else minimum\n\n        return self.cache[remainder]\n#         if not coins:\n#             return 0\n#         dp = [float(\\"inf\\") for _ in range(amount + 1)]\n        \n#         dp[0]=0\n#         for i in range(1,amount+1):\n#             for coin in coins:\n#                 if i>=coin:\n#                     dp[i] = min(dp[i],dp[i-coin]+1)\n#         if dp[amount]!= float(\\"inf\\"):\n#             return dp[-1]\n#         else:\n#             return -1\n            \n#         \\"\\"\\"\n#         #1  Return 0 if there are no given coins\n#         \\"\\"\\"\n#         if not coins:\n#             return 0\n        \n#         \\"\\"\\"\n#         #2  Initialize a \'dp\' array of a size of the given amount (inclusive, hence +1).\n#         #   Initialize each index element to be an arbitary number. In this case I chose amount + 1. E.g.: 11 + 1 = 12\n#         \\"\\"\\"\n#         dp = [float(\\"inf\\") for _ in range(amount + 1)]\n        \n#         \\"\\"\\"\n#         #3  Base case. Make the first cell 0 because if amount is 0, you do not need any coin to make up to that amount\n#         #   stdout: dp = [0, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12]\n#         \\"\\"\\"\n#         dp[0] = 0\n        \n#         \\"\\"\\"\n#         #4  Look through the entire \'dp\' array, for each of the index element, we will check it against the list(array) of given coins.\n#         #   \'i\' in this case is the amount we want to compute from bottom-up starting from 0 to the \'amount\' that the question asks for\n#         #   E.g.: [0, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12] vs [1, 2, 5]\n#                    ^                   ^                           ^             \n#                    amount 0            amount 5                    amount = 11 (this is what we want)             \n#         \\"\\"\\"\n#         for i in range(1, amount+1):\n#             for coin in coins:\n#                 \\"\\"\\"\n#                 #5  If \'i\' (the current amount we want to find, is less than \'coin\', we will skip that. Otherwise compute it:\n#                 #   Because it does not make sense to compute the coin if the coin itself is already larger than the amount that we\'re looking at\n#                 \\"\\"\\"\n#                 if i >= coin:\n#                     \\"\\"\\"\n#                     #6  We shall update each dp[i] to be the minimum between itself vs it\'s previous computed answer dp[i-coin]. \n#                     #   And we do this for each available coin. Only if \'coin\' is smaller than the amount \'i\'\n#                     #   We do \'+1\' for dp[i-coin] + 1 here because it costs us a step to do so\n#                     \\"\\"\\"\n#                     dp[i] = min(dp[i], dp[i-coin] + 1)\n        \n#         \\"\\"\\"\n#         #7  By the end of the 2 for loops, you will end up with \n#         #   stdout: [0, 1, 1, 2, 2, 1, 2, 2, 3, 3, 2, 3]\n        \n#         #8  So if the dp[amount] is not the original amount we initialized at Step #3. Then we shall return the dp[amount] that was asked by the question\n#         \\"\\"\\"\n#         if dp[amount] != float(\\"inf\\"):\n#             return dp[amount]\n#         else:\n#             return -1\n        \n#         \\"\\"\\"\n#         #9  Else. If the dp[amount] is still amount + 1 as we initialized. It means there were no suitable coins for this scenario and -1 is returned\n#         \\"\\"\\"\n    \n#         # key:amount value:min number of coins for the amount\n    \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: 8604