<p>You are given an <code>m x n</code> grid <code>grid</code> where:</p>

<ul>
	<li><code>&#39;.&#39;</code> is an empty cell.</li>
	<li><code>&#39;#&#39;</code> is a wall.</li>
	<li><code>&#39;@&#39;</code> is the starting point.</li>
	<li>Lowercase letters represent keys.</li>
	<li>Uppercase letters represent locks.</li>
</ul>

<p>You start at the starting point and one move consists of walking one space in one of the four cardinal directions. You cannot walk outside the grid, or walk into a wall.</p>

<p>If you walk over a key, you can pick it up and you cannot walk over a lock unless you have its corresponding key.</p>

<p>For some <code><font face="monospace">1 &lt;= k &lt;= 6</font></code>, there is exactly one lowercase and one uppercase letter of the first <code>k</code> letters of the English alphabet in the grid. This means that there is exactly one key for each lock, and one lock for each key; and also that the letters used to represent the keys and locks were chosen in the same order as the English alphabet.</p>

<p>Return <em>the lowest number of moves to acquire all keys</em>. If it is impossible, return <code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-keys2.jpg" style="width: 404px; height: 245px;" />
<pre>
<strong>Input:</strong> grid = [&quot;@.a..&quot;,&quot;###.#&quot;,&quot;b.A.B&quot;]
<strong>Output:</strong> 8
<strong>Explanation:</strong> Note that the goal is to obtain all the keys not to open all the locks.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-key2.jpg" style="width: 404px; height: 245px;" />
<pre>
<strong>Input:</strong> grid = [&quot;@..aA&quot;,&quot;..B#.&quot;,&quot;....b&quot;]
<strong>Output:</strong> 6
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-keys3.jpg" style="width: 244px; height: 85px;" />
<pre>
<strong>Input:</strong> grid = [&quot;@Aa&quot;]
<strong>Output:</strong> -1
</pre>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 30</code></li>
	<li><code>grid[i][j]</code> is either an English letter, <code>&#39;.&#39;</code>, <code>&#39;#&#39;</code>, or <code>&#39;@&#39;</code>.&nbsp;</li>
	<li>There is exactly one&nbsp;<code>&#39;@&#39;</code>&nbsp;in the grid.</li>
	<li>The number of keys in the grid is in the range <code>[1, 6]</code>.</li>
	<li>Each key in the grid is <strong>unique</strong>.</li>
	<li>Each key in the grid has a matching lock.</li>
</ul>

class Solution {
public:
    int shortestPathAllKeys(vector<string>& grid) {
        int n=grid.size(), m=grid[0].size();
        vector<vector<vector<int>>> vst(n,vector<vector<int>>(m,vector<int>(1<<6,0)));
        int cnt=0;
        int tmpi, tmpj;
        for(int i=0; i<n; i++){
            for(int j=0; j<m; j++){
                if(grid[i][j]>='a' && grid[i][j]<='f')cnt++;
                else if(grid[i][j]=='@')tmpi=i, tmpj=j;
            }
        }
        vector<int> di={-1,0,0,1};
        vector<int> dj={0,-1,1,0};
        queue<vector<int>> q;
        q.push({tmpi,tmpj,0});
        vst[tmpi][tmpj][0]=1;
        int ans=0;
        while(!q.empty()){
            int tmp=q.size();
            while(tmp--){
                auto it=q.front();
                q.pop();
                int i=it[0], j=it[1], keys=it[2];
                if(keys==(1<<cnt)-1)return ans;
                for(int k=0; k<4; k++){
                    int newi=i+di[k], newj=j+dj[k];
                    if(newi>=0 && newi<n && newj>=0 && newj<m && grid[newi][newj]!='#'){
                        int newKeys = keys;
                        if (grid[newi][newj] >= 'a' && grid[newi][newj] <= 'f') {
                            newKeys |= (1 << (grid[newi][newj] - 'a'));
                        }
                        if(vst[newi][newj][newKeys])continue;
                        if(grid[newi][newj]>='A' && grid[newi][newj]<='F'){
                            if((keys>>(grid[newi][newj]-'A'))&1){
                                q.push({newi,newj,newKeys});
                                vst[newi][newj][newKeys]=1;
                            }
                        }else{
                            q.push({newi,newj,newKeys});
                            vst[newi][newj][newKeys]=1;
                        }
                    }
                }
            }
            ans++;
        }
        // int ans=solve(tmpi,tmpj,0,grid,n,m,vst);
        // if(ans!=INT_MAX)return ans;
        return -1;
    }
};
33000