<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 m=grid.size(),n=grid[0].size();
        map<pair<int,pair<int,int>>,int>vis;
        queue<pair<pair<int,int>,pair<int,int>>>qu;
        int sx=-1,sy=-1,keys=0;
        for(int i=0;i<m;i++)
        {
            for(int j=0;j<n;j++)
            {
                if(grid[i][j]=='@'){
                    sx=i;sy=j;
                }
                if(grid[i][j]>=97&&grid[i][j]<=122) keys++;
            }
        }
        qu.push({{0,0},{sx,sy}});
        vis[{0,{sx,sy}}]=1;
        int totmask=(1<<keys);
        vector<vector<int>>dir={{0,1},{1,0},{-1,0},{0,-1}};
        while(!qu.empty())
        {
            auto it=qu.front();
            qu.pop();
            int moves=it.first.first,mask=it.first.second,i=it.second.first,j=it.second.second;
            //cout<<mask<<" "<<i<<" "<<j<<endl;
            if(totmask-1==mask){return moves;}
            for(auto d:dir){
                int ni=i+d[0],nj=j+d[1];
                if(ni<m&&ni>=0&&nj>=0&&nj<n&&(grid[ni][nj]!='#'))
                {
                    if(grid[ni][nj]>=97&&grid[ni][nj]<=122){
                        int nmask=mask|(1<<(grid[ni][nj]-'a'));
                        if(!vis[{nmask,{ni,nj}}]){
                            vis[{nmask,{ni,nj}}]=1;
                            qu.push({{moves+1,nmask},{ni,nj}});
                        }
                    }
                    else if(grid[ni][nj]>=65&&grid[ni][nj]<=90){
                        if(!vis[{mask,{ni,nj}}]&&(mask&(1<<(grid[ni][nj]-'A')))>0){
                            vis[{mask,{ni,nj}}]=1;
                            qu.push({{moves+1,mask},{ni,nj}});
                        }
                    }
                    else{
                        if(!vis[{mask,{ni,nj}}]){
                            vis[{mask,{ni,nj}}]=1;
                            qu.push({{moves+1,mask},{ni,nj}});
                        }
                    }
                }
            }
        }
        return -1;
    }
};
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