<p>You are given an integer array <code>coins</code> representing coins of different denominations and an integer <code>amount</code> representing a total amount of money.</p>

<p>Return <em>the fewest number of coins that you need to make up that amount</em>. If that amount of money cannot be made up by any combination of the coins, return <code>-1</code>.</p>

<p>You may assume that you have an infinite number of each kind of coin.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> coins = [1,2,5], amount = 11
<strong>Output:</strong> 3
<strong>Explanation:</strong> 11 = 5 + 5 + 1
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> coins = [2], amount = 3
<strong>Output:</strong> -1
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> coins = [1], amount = 0
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= coins.length &lt;= 12</code></li>
	<li><code>1 &lt;= coins[i] &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>0 &lt;= amount &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def coinChange(self, coins: List[int], amount: int) -> int:
        if amount == 0:
            return 0
        #next block doesnt work
        '''
        coins.sort(reverse=True)
        res = 0
        for coin in coins:
            if amount//coin:
                temp, amount = divmod(amount, coin)
                res += temp
        if amount == 0:
            return res
        else:
            return -1
        '''
        coins.sort(reverse=True)
        partial = Counter(coins)
        for coin1 in coins:
            for coin2 in coins:
                val = coin1+coin2
                if val in partial:
                    partial[val] = min(partial[val], 2)
                val = 2*coin1+coin2
                if val in partial:
                    partial[val] = min(partial[val], 3)
                val = 3*coin1+coin2
                if val in partial:
                    partial[val] = min(partial[val], 4)
                val = 4*coin1+coin2
                if val in partial:
                    partial[val] = min(partial[val], 5)
                val = 5*coin1+coin2
                if val in partial:
                    partial[val] = min(partial[val], 6)

        def recursive(amount):
            res = 2**32
            if amount < min(coins):
                return res
            if amount in partial.keys():
                #print(f"amount found {amount} {partial[amount]}")
                return partial[amount]

            for c in coins:
                res = min(res, recursive(amount-c)+1)
            partial[amount] = res
            return res
        res = recursive(amount)
        if res == 2**32:
                return -1
        return res
#[186,419,83,408]
#6249        
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