<p>We are given <code>n</code> different types of <code>stickers</code>. Each sticker has a lowercase English word on it.</p>

<p>You would like to spell out the given string <code>target</code> by cutting individual letters from your collection of stickers and rearranging them. You can use each sticker more than once if you want, and you have infinite quantities of each sticker.</p>

<p>Return <em>the minimum number of stickers that you need to spell out </em><code>target</code>. If the task is impossible, return <code>-1</code>.</p>

<p><strong>Note:</strong> In all test cases, all words were chosen randomly from the <code>1000</code> most common US English words, and <code>target</code> was chosen as a concatenation of two random words.</p>

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

<pre>
<strong>Input:</strong> stickers = [&quot;with&quot;,&quot;example&quot;,&quot;science&quot;], target = &quot;thehat&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong>
We can use 2 &quot;with&quot; stickers, and 1 &quot;example&quot; sticker.
After cutting and rearrange the letters of those stickers, we can form the target &quot;thehat&quot;.
Also, this is the minimum number of stickers necessary to form the target string.
</pre>

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

<pre>
<strong>Input:</strong> stickers = [&quot;notice&quot;,&quot;possible&quot;], target = &quot;basicbasic&quot;
<strong>Output:</strong> -1
Explanation:
We cannot form the target &quot;basicbasic&quot; from cutting letters from the given stickers.
</pre>

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

<ul>
	<li><code>n == stickers.length</code></li>
	<li><code>1 &lt;= n &lt;= 50</code></li>
	<li><code>1 &lt;= stickers[i].length &lt;= 10</code></li>
	<li><code>1 &lt;= target.length &lt;= 15</code></li>
	<li><code>stickers[i]</code> and <code>target</code> consist of lowercase English letters.</li>
</ul>

class Solution {
public:
int minStickersHelper(vector<vector<int>>& stickerCounts, vector<int>& targetCount, unordered_map<string, int>& memo) {
    string key = "";
    for (int i = 0; i < 26; ++i) {
        key += string(targetCount[i], 'a' + i);
    }
    
    if (key == "") return 0;
    
    if (memo.find(key) != memo.end()) return memo[key];
    
    int minStickers = INT_MAX;
    
    for (auto& sticker : stickerCounts) {

        if (sticker[key[0] - 'a'] == 0) continue;
        
        vector<int> newTargetCount = targetCount;
        for (int i = 0; i < 26; ++i) {
            newTargetCount[i] = max(0, newTargetCount[i] - sticker[i]);
        }
        
        int next = minStickersHelper(stickerCounts, newTargetCount, memo);
        if (next != -1) {
            minStickers = min(minStickers, 1 + next);
        }
    }
    memo[key] = (minStickers == INT_MAX) ? -1 : minStickers;
    return memo[key];
}

    int minStickers(vector<string>& stickers, string target) {
        int n = stickers.size();
    vector<vector<int>> stickerCounts(n, vector<int>(26, 0));
    
    for (int i = 0; i < n; ++i) {
        for (char c : stickers[i]) {
            stickerCounts[i][c - 'a']++;
        }
    }
    
    vector<int> targetCount(26, 0);
    for (char c : target) {
        targetCount[c - 'a']++;
    }
    
    unordered_map<string, int> memo;
    
    return minStickersHelper(stickerCounts, targetCount, memo);
    }
};
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