<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:
bool isvalid(int i,int j,int &mask,vector<vector<vector<int>>>&dp,vector<string>& grid){
    int n=grid.size();
    int m=grid[0].size();
    if(i<0||i>=n||j<0||j>=m)return false;
    if(dp[i][j][mask]!=-1)return false;
    if(grid[i][j]=='#')return false;
    if(grid[i][j]>='A'&&grid[i][j]<='F') return (1<<(grid[i][j]-'A'))&mask;
    if(grid[i][j]>='a'&&grid[i][j]<='f')mask=mask|(1<<(grid[i][j]-'a'));
    return true;
}
int ans(int i,int j,int mask,int target,vector<vector<vector<int>>>&dp,vector<string>& grid){
   dp[i][j][mask]=0;
   queue<pair<pair<int,int>,int>> q;
   q.push(make_pair(make_pair(i,j),0));
   while(!q.empty()){
    i=q.front().first.first;
    j=q.front().first.second;

    mask=q.front().second;
    q.pop();
    int l=dp[i][j][mask];
    int mask2=mask;
    if(isvalid(i,j+1,mask,dp,grid)){
        int curr=1+l;
        if(mask==target)return curr;
        dp[i][j+1][mask]=curr;
        q.push(make_pair(make_pair(i,j+1),mask));
    }
    mask=mask2;
    if(isvalid(i+1,j,mask,dp,grid)){
        int curr=1+l;
        if(mask==target)return curr;
        dp[i+1][j][mask]=curr;
        q.push(make_pair(make_pair(i+1,j),mask));
    }
    mask=mask2;
    if(isvalid(i,j-1,mask,dp,grid)){
        int curr=1+l;
        if(mask==target)return curr;
        dp[i][j-1][mask]=curr;
        q.push(make_pair(make_pair(i,j-1),mask));
    }
    mask=mask2;
    if(isvalid(i-1,j,mask,dp,grid)){
        int curr=1+l;
        if(mask==target)return curr;
        dp[i-1][j][mask]=curr;
        q.push(make_pair(make_pair(i-1,j),mask));
    }
   }
   return INT_MAX;
}
    int shortestPathAllKeys(vector<string>& grid) {
        int target=0;
        int index1,index2;
        int n=grid.size(),m=grid[0].size();
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
               if(grid[i][j]=='@'){
                index1=i,index2=j;
               }
               if(grid[i][j]>='a'&&grid[i][j]<='f'){
                target|=(1<<(grid[i][j]-'a'));
               }
            }
        }
        vector<vector<vector<int>>> dp(n,vector<vector<int>>(m,vector<int>(target+1,-1)));
        int a=ans(index1,index2,0,target,dp,grid);
        if(a==INT_MAX)return -1;
        return a;
    }
};
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