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 = "\nclass Solution:\n    def back_tracking_solution(self):\n        def _is_solution(amount_left):\n            if amount_left == 0:\n                return True\n            return False\n        \n        def _process_solution(num_coins_used, fewest_coins):\n            if num_coins_used < fewest_coins[0]:\n                fewest_coins[0] = num_coins_used\n        \n        def _candidate_coins_start_idx(amount_left, coins, current_coin_start_idx):                 \n            for i in range(current_coin_start_idx, len(coins)):\n                if amount_left >= coins[i]:\n                    return i\n                \n            return None\n        \n        def _backtrack(amount_left, num_coins_used, current_fewest_coins, coins, current_coin_start_idx):\n            if _is_solution(amount_left):\n                _process_solution(num_coins_used, current_fewest_coins)\n            else:\n                real_coin_start_idx = _candidate_coins_start_idx(amount_left, coins, current_coin_start_idx)\n                if real_coin_start_idx is not None:\n                    for i in range(real_coin_start_idx, len(coins)):\n                        _backtrack(amount_left - coins[i], num_coins_used + 1, current_fewest_coins, coins, i)\n        \n        return _backtrack\n    \n    def dynamic_programming_solution(self):\n        def _dp_bad(amount, coins):\n            sorted_coins = sorted(coins)\n            cache = [[float('inf')] * len(coins) for i in range(amount + 1)]\n            \n            for denom_idx in range(len(sorted_coins)):\n                cache[0][denom_idx] = 0\n            \n            for amt in range(amount + 1):\n                cache[amt][0] = (amt // sorted_coins[0]) if ((amt % sorted_coins[0]) == 0) else float('inf')\n            \n            #print(f'first: {cache}')\n            for i in range(1, len(cache)):\n                for j in range(1, len(sorted_coins)):\n                    max_num_of_denom = (i // sorted_coins[j]) + 1\n                    for k in range(max_num_of_denom):\n                        #print(f'BEFORE: i: {i}, j:{j}, k: {k}, each: {cache}')\n                        cache[i][j] = min(cache[i][j], k + cache[i - (k*sorted_coins[j])][j-1])\n                        #print(f'AFTER: i: {i}, j:{j}, k: {k}, each: {cache}')\n                        \n            \n            #for idx, change in enumerate(cache):\n                #print(f'amount: {idx}, change: {change}')\n            \n            return cache[amount][-1]\n        \n        def _dp_cache_recursive(amount, coins, cache):\n            if amount in cache:\n                return cache[amount]\n            \n            for c in coins:\n                if (amount >= c):\n                    intermediate = 1 + _dp_cache_recursive(amount - c, coins, cache)\n                    if amount in cache:\n                        cache[amount] = min(cache[amount], intermediate)\n                    else:\n                        cache[amount] = intermediate\n            \n            return cache[amount] if (amount in cache) else float('inf')\n    \n        def _dp_bottom_up_1(amount, coins):\n            sorted_coins = sorted(coins)\n            \n            cache = [[float('inf')] * len(coins) for i in range(amount + 1)]\n            \n            for denom_idx in range(len(sorted_coins)):\n                cache[0][denom_idx] = 0\n            \n            for amt in range(1, len(cache)):\n                for denom_idx in range(len(sorted_coins)):\n                    amt_left = amt - sorted_coins[denom_idx]\n                    \n                    if (amt_left >= 0):\n                        cache[amt][denom_idx] = 1 + min(cache[amt_left][0:(denom_idx + 1)])\n            \n            #for amt, num in enumerate(cache):\n                #print(f'amount: {amt}, num: {num}')\n            \n            return min(cache[amount])\n        \n        return _dp_bottom_up_1\n        \n        \n    def coinChange(self, coins: List[int], amount: int) -> int:\n        # backtracking solution\n        # fewest_coins = [float('inf')]\n        # coins_sorted_desc = sorted(coins, reverse = True)\n        # self.back_tracking_solution()(amount, 0, fewest_coins, coins_sorted_desc, 0)\n        # return -1 if fewest_coins[0] == float('inf') else fewest_coins[0]\n    \n        # Dynamic Programming - recursive call result caching\n        # result = self.dynamic_programming_solution()(amount, coins, cache = {0: 0})\n        # return -1 if (result == float('inf')) else result\n        \n        # Dynamic Programming - non-recursive bottom-up version 1\n        result = self.dynamic_programming_solution()(amount, coins)\n        return -1 if (result == float('inf')) else result"
_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: 7954