<p>You are given a string <code>s</code> of length <code>n</code> where <code>s[i]</code> is either:</p>

<ul>
	<li><code>&#39;D&#39;</code> means decreasing, or</li>
	<li><code>&#39;I&#39;</code> means increasing.</li>
</ul>

<p>A permutation <code>perm</code> of <code>n + 1</code> integers of all the integers in the range <code>[0, n]</code> is called a <strong>valid permutation</strong> if for all valid <code>i</code>:</p>

<ul>
	<li>If <code>s[i] == &#39;D&#39;</code>, then <code>perm[i] &gt; perm[i + 1]</code>, and</li>
	<li>If <code>s[i] == &#39;I&#39;</code>, then <code>perm[i] &lt; perm[i + 1]</code>.</li>
</ul>

<p>Return <em>the number of <strong>valid permutations</strong> </em><code>perm</code>. Since the answer may be large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;DID&quot;
<strong>Output:</strong> 5
<strong>Explanation:</strong> The 5 valid permutations of (0, 1, 2, 3) are:
(1, 0, 3, 2)
(2, 0, 3, 1)
(2, 1, 3, 0)
(3, 0, 2, 1)
(3, 1, 2, 0)
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;D&quot;
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>n == s.length</code></li>
	<li><code>1 &lt;= n &lt;= 200</code></li>
	<li><code>s[i]</code> is either <code>&#39;I&#39;</code> or <code>&#39;D&#39;</code>.</li>
</ul>

using ll = long long;

ll dp[205][205];
const ll mod = 1e9 + 7;
int n;

ll solve(int index, string &s, vector<int> &v, int piche)
{
    if (index >= s.size())
        return 1;

    if (dp[index][piche] != -1)
        return dp[index][piche];

    dp[index][piche] = 0;

    if (s[index] == 'D')
    {
        for (int i = 0; i < piche; ++i)
        {
            if (v[i] == 0)
            {
                v[i] = 1;
                dp[index][piche] += solve(index + 1, s, v, i);
                dp[index][piche] %= mod;
                v[i] = 0;
            }
        }
    }
    else
    {
        for (int i = piche + 1; i < n + 1; ++i)
        {
            if (v[i] == 0)
            {
                v[i] = 1;
                dp[index][piche] += solve(index + 1, s, v, i);
                dp[index][piche] %= mod;
                v[i] = 0;
            }
        }
    }

    return dp[index][piche] %= mod;

}

class Solution
{
    public:
        int numPermsDISequence(string s)
        {
            memset(dp, -1, sizeof(dp));
            n=s.size();
            
            if(n==1)
                return 1;
            
            vector<int>v(n+1,0);
            
            ll ans=0;
            
            for(int i=0;i<=n;++i)
            {
                v[i]=1;
                ans+=solve(0,s,v,i);
                ans%=mod;
                v[i]=0;
            }
            return ans;
            
        }
};
8200