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        #In any dp probelm we need to identify the recursive relationship. \n        #The solution to a problem can be found with teh help of its sub problems. \n        '''\n        In this case we define teh recursive relationship as follows:\n        Where Opt(S) is the minimum number of coins in [c1, c2, .., cn] that are needed to create amount S. \n        \n        The following recursive relationship holds:\n        Opt(S) = Opt(S - C) + 1, where C is the denomination of [c0, c1, ..., cn-1] and S is the amount.   \n        \n        Minimum number of coins for amoun S in denomination cn, is given by the minimum amount of (amount - previouse denomination) for all coins.  \n        \n        But we dont know the denomination of the last coin C, so we compute \n        Opt(S - ci) for all possible denominations c0, c1, ..., cn, and choose the minimum among them. \n        \n        Subject to S - ci >= 0. \n        \n        Base cases:\n        Opt(S) = 0, when S = 0. S is the amount.\n        Opt(S) = -1, when n = 0. \n        \n        * Each sub porblem (coin) has S computations. \n        * And the number of subproblems is O(n * S). \n        \n        '''\n        #What will we identify subproblems by. (S - ci)\n        #or by an amount. So as we are calculating the minimum number of coind needed for each amount, we need to look at the minimum number of coins need using c0, c1, .., cn. \n        #Sub problems are determined by amounts, so we cache them by amount. \n        #Fir every sub problem need optimal number of coins for each denomination. Then we take the minimum of all teh minimums, and that is the minimum number of coins needed to represnet an amount. \n        \n        \n        T = [float('inf')] * (amount + 1)\n        T[0] = 0\n\n        #In an iteratoive solution we move left to right and have to compute teh minimum number of coins for all amounts before this one. \n        \n        for amnt in range(1, amount + 1):\n            curr_min = float('inf')\n            for k in range(len(coins)):\n                #calculate the minimum number of coins needed for each denotion to represnet the amount given by amnt. \n                #then take minimum and assign it to T[amnt].\n                if coins[k] <= amnt:\n                    val = 1 + T[amnt - coins[k]]\n                    if val < curr_min:\n                        curr_min = val\n            \n            T[amnt] = curr_min\n\n        return -1 if T[-1] == float('inf') else T[-1]\n                \n        \n        \n        \n            \n        \n        \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: 5716