<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:
    vector<int> cnt_t;
    int solve(vector<vector<int>> &cnt_s, vector<unordered_map<string, int>> &dp, int i) {
        string mask;
        for (int j = 0; j < cnt_t.size(); j++) {
            for (int k = 0; k < cnt_t[j]; k++)
                mask += (j + 'a');
        }
        if (mask == "")
            return 0;
        if (i >= cnt_s.size())
            return INT_MAX;
        sort(mask.begin(), mask.end());
        if (dp[i].count(mask))
            return dp[i][mask];
        dp[i][mask] = solve(cnt_s, dp, i + 1);
        int max_cnt = 0;
        for (int j = 0; j < 26; j++) {
            if (cnt_s[i][j] && cnt_t[j])
                max_cnt = max(max_cnt, (cnt_s[i][j] + cnt_t[j] - 1) / cnt_s[i][j]);
        }
        // cout << i << " " << max_cnt << endl;
        for (int j = 1; j <= max_cnt; j++) {
            for (int k = 0; k < 26; k++)
                cnt_t[k] -= cnt_s[i][k];
            int val = solve(cnt_s, dp, i + 1);
            if (val != INT_MAX)
                dp[i][mask] = min(dp[i][mask], j + val);
        }
        for (int j = 1; j <= max_cnt; j++) {
            for (int k = 0; k < 26; k++)
                cnt_t[k] += cnt_s[i][k];
        }

        return dp[i][mask];
    }
    int minStickers(vector<string> &stickers, string target) {
        int n = stickers.size();
        vector<unordered_map<string, int>> dp(n);
        vector<vector<int>> cnt_s(n, vector<int>(26));
        cnt_t = vector<int>(26);
        for (int i = 0; i < n; i++) {
            for (auto &c : stickers[i])
                cnt_s[i][c - 'a']++;
        }
        for (auto &c : target)
            cnt_t[c - 'a']++;
        int res = solve(cnt_s, dp, 0);
        return res == INT_MAX ? -1 : res;
    }
};
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