<p>You are given an array of <code>words</code> where each word consists of lowercase English letters.</p>

<p><code>word<sub>A</sub></code> is a <strong>predecessor</strong> of <code>word<sub>B</sub></code> if and only if we can insert <strong>exactly one</strong> letter anywhere in <code>word<sub>A</sub></code> <strong>without changing the order of the other characters</strong> to make it equal to <code>word<sub>B</sub></code>.</p>

<ul>
	<li>For example, <code>&quot;abc&quot;</code> is a <strong>predecessor</strong> of <code>&quot;ab<u>a</u>c&quot;</code>, while <code>&quot;cba&quot;</code> is not a <strong>predecessor</strong> of <code>&quot;bcad&quot;</code>.</li>
</ul>

<p>A <strong>word chain</strong><em> </em>is a sequence of words <code>[word<sub>1</sub>, word<sub>2</sub>, ..., word<sub>k</sub>]</code> with <code>k &gt;= 1</code>, where <code>word<sub>1</sub></code> is a <strong>predecessor</strong> of <code>word<sub>2</sub></code>, <code>word<sub>2</sub></code> is a <strong>predecessor</strong> of <code>word<sub>3</sub></code>, and so on. A single word is trivially a <strong>word chain</strong> with <code>k == 1</code>.</p>

<p>Return <em>the <strong>length</strong> of the <strong>longest possible word chain</strong> with words chosen from the given list of </em><code>words</code>.</p>

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

<pre>
<strong>Input:</strong> words = [&quot;a&quot;,&quot;b&quot;,&quot;ba&quot;,&quot;bca&quot;,&quot;bda&quot;,&quot;bdca&quot;]
<strong>Output:</strong> 4
<strong>Explanation</strong>: One of the longest word chains is [&quot;a&quot;,&quot;<u>b</u>a&quot;,&quot;b<u>d</u>a&quot;,&quot;bd<u>c</u>a&quot;].
</pre>

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

<pre>
<strong>Input:</strong> words = [&quot;xbc&quot;,&quot;pcxbcf&quot;,&quot;xb&quot;,&quot;cxbc&quot;,&quot;pcxbc&quot;]
<strong>Output:</strong> 5
<strong>Explanation:</strong> All the words can be put in a word chain [&quot;xb&quot;, &quot;xb<u>c</u>&quot;, &quot;<u>c</u>xbc&quot;, &quot;<u>p</u>cxbc&quot;, &quot;pcxbc<u>f</u>&quot;].
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;abcd&quot;,&quot;dbqca&quot;]
<strong>Output:</strong> 1
<strong>Explanation:</strong> The trivial word chain [&quot;abcd&quot;] is one of the longest word chains.
[&quot;abcd&quot;,&quot;dbqca&quot;] is not a valid word chain because the ordering of the letters is changed.
</pre>

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

<ul>
	<li><code>1 &lt;= words.length &lt;= 1000</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 16</code></li>
	<li><code>words[i]</code> only consists of lowercase English letters.</li>
</ul>

#define Max 1e6
#define ff first
#define ss second
#define ll int
#define pb push_back
#define ppb pop_back
#define pf push_front
#define ppf pop_front
#define mp make_pair
#define pii pair<ll, ll>
#define vi vector<ll>
#define v vector
#define mii map<ll, ll>
#define umap unordered_map
#define pq priority_queue<ll>
#define pqm priority_queue<ll, vi, greater<ll>>
#define setbits(x) __builtin_popcountll(x)
#define zrobits(x) __builtin_ctzll(x)
#define mod 1000000007
#define inf 1e18
#define ps(x, y) fixed << setprecision(y) << x
#define mk(arr, n, type) type *arr = new type[n];
#define all(x) x.begin(), x.end()
#define sp ' '
#define endl '\n'
#define pi 3.14159265359
#define intmax INT32_MAX
#define intmin INT32_MIN
#define conti continue
#define null NULL
#define sc(x) static_cast<x>

class Solution {
public:
bool fun1(string &w1, string &w2)
{
    ll n = w1.length();
    ll m = w2.length();
    if (m - n != 1)
    {
        return false;
    }
    ll c = 0;
    ll i = 0;
    ll j = 0;
    while (i < n && j < m)
    {
        if (w1[i] == w2[j])
        {
            i++;
            j++;
        }
        else
        {
            c++;
            j++;
        }
    }
    if (c == 0)
        return j == n;
    return (i == n && j == m && c == 1);
}
ll fun(v<string> &a, ll i, ll prev,v<v<ll>> &dp)
{
    ll n = a.size();
    if (i >= n)
        return 0;
    if(dp[i][prev+1]!=-1)
        return dp[i][prev+1];
    ll ans1 = fun(a, i + 1, prev, dp);
    ll ans2 = 0;
    if (prev == -1 || fun1(a[prev], a[i]))
        ans2 = 1 + fun(a, i + 1, i, dp);
    return dp[i][prev+1]=max(ans1, ans2);
}
int longestStrChain(vector<string> &words)
{
    sort(all(words), [&](string a, string b)
         {
        if(a.length()==b.length())
            return a<b;
        return a.length()<b.length(); });
    ll n=words.size();
    v<v<ll>> dp(n,v<ll>(n+1,-1));
    return fun(words, 0, -1,dp);
}
};
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